diff --git a/crates/polars-lazy/src/frame/mod.rs b/crates/polars-lazy/src/frame/mod.rs
index 99ddd979d65b..d7b11f7ab7fa 100644
--- a/crates/polars-lazy/src/frame/mod.rs
+++ b/crates/polars-lazy/src/frame/mod.rs
@@ -392,9 +392,10 @@ impl LazyFrame {
     ///
     /// `existing` and `new` are iterables of the same length containing the old and
     /// corresponding new column names. Renaming happens to all `existing` columns
-    /// simultaneously, not iteratively. (In particular, all columns in `existing` must
-    /// already exist in the `LazyFrame` when `rename` is called.)
-    pub fn rename<I, J, T, S>(self, existing: I, new: J) -> Self
+    /// simultaneously, not iteratively. If `strict` is true, all columns in `existing`
+    /// must be present in the `LazyFrame` when `rename` is called; otherwise, only
+    /// those columns that are actually found will be renamed (others will be ignored).
+    pub fn rename<I, J, T, S>(self, existing: I, new: J, strict: bool) -> Self
     where
         I: IntoIterator<Item = T>,
         J: IntoIterator<Item = S>,
@@ -420,6 +421,7 @@ impl LazyFrame {
         self.map_private(DslFunction::Rename {
             existing: existing_vec.into(),
             new: new_vec.into(),
+            strict,
         })
     }
 
diff --git a/crates/polars-lazy/src/tests/cse.rs b/crates/polars-lazy/src/tests/cse.rs
index 9122ba3814ff..6ed8e1cc67c8 100644
--- a/crates/polars-lazy/src/tests/cse.rs
+++ b/crates/polars-lazy/src/tests/cse.rs
@@ -307,7 +307,7 @@ fn test_cse_columns_projections() -> PolarsResult<()> {
 
     let left = left.cross_join(right.clone().select([col("A")]), None);
     let q = left.join(
-        right.rename(["B"], ["C"]),
+        right.rename(["B"], ["C"], true),
         [col("A"), col("C")],
         [col("A"), col("C")],
         JoinType::Left.into(),
diff --git a/crates/polars-lazy/src/tests/optimization_checks.rs b/crates/polars-lazy/src/tests/optimization_checks.rs
index 4a99413d48cc..51a6bf26cfb0 100644
--- a/crates/polars-lazy/src/tests/optimization_checks.rs
+++ b/crates/polars-lazy/src/tests/optimization_checks.rs
@@ -323,7 +323,7 @@ fn test_lazy_filter_and_rename() {
     let lf = df
         .clone()
         .lazy()
-        .rename(["a"], ["x"])
+        .rename(["a"], ["x"], true)
         .filter(col("x").map(
             |s: Column| Ok(Some(s.as_materialized_series().gt(3)?.into_column())),
             GetOutput::from_type(DataType::Boolean),
@@ -337,7 +337,7 @@ fn test_lazy_filter_and_rename() {
     assert!(lf.collect().unwrap().equals(&correct));
 
     // now we check if the column is rename or added when we don't select
-    let lf = df.lazy().rename(["a"], ["x"]).filter(col("x").map(
+    let lf = df.lazy().rename(["a"], ["x"], true).filter(col("x").map(
         |s: Column| Ok(Some(s.as_materialized_series().gt(3)?.into_column())),
         GetOutput::from_type(DataType::Boolean),
     ));
diff --git a/crates/polars-plan/src/plans/functions/dsl.rs b/crates/polars-plan/src/plans/functions/dsl.rs
index fd4b740af9df..c72e4ebe3c06 100644
--- a/crates/polars-plan/src/plans/functions/dsl.rs
+++ b/crates/polars-plan/src/plans/functions/dsl.rs
@@ -42,6 +42,7 @@ pub enum DslFunction {
     Rename {
         existing: Arc<[PlSmallStr]>,
         new: Arc<[PlSmallStr]>,
+        strict: bool,
     },
     Unnest(Vec<Selector>),
     Stats(StatsFunction),
@@ -119,10 +120,15 @@ impl DslFunction {
                 offset,
                 schema: Default::default(),
             },
-            DslFunction::Rename { existing, new } => {
+            DslFunction::Rename {
+                existing,
+                new,
+                strict,
+            } => {
                 let swapping = new.iter().any(|name| input_schema.get(name).is_some());
-                validate_columns_in_input(existing.as_ref(), input_schema, "rename")?;
-
+                if strict {
+                    validate_columns_in_input(existing.as_ref(), input_schema, "rename")?;
+                }
                 FunctionIR::Rename {
                     existing,
                     new,
diff --git a/crates/polars-python/src/lazyframe/general.rs b/crates/polars-python/src/lazyframe/general.rs
index b5e9bfc7bd50..b9ca9c8cf74d 100644
--- a/crates/polars-python/src/lazyframe/general.rs
+++ b/crates/polars-python/src/lazyframe/general.rs
@@ -964,9 +964,9 @@ impl PyLazyFrame {
         ldf.with_columns_seq(exprs.to_exprs()).into()
     }
 
-    fn rename(&mut self, existing: Vec<String>, new: Vec<String>) -> Self {
+    fn rename(&mut self, existing: Vec<String>, new: Vec<String>, strict: bool) -> Self {
         let ldf = self.ldf.clone();
-        ldf.rename(existing, new).into()
+        ldf.rename(existing, new, strict).into()
     }
 
     fn reverse(&self) -> Self {
diff --git a/crates/polars-sql/src/context.rs b/crates/polars-sql/src/context.rs
index e95bda62916d..342a5e0883d2 100644
--- a/crates/polars-sql/src/context.rs
+++ b/crates/polars-sql/src/context.rs
@@ -751,6 +751,7 @@ impl SQLContext {
                 lf = lf.rename(
                     select_modifiers.rename.keys(),
                     select_modifiers.rename.values(),
+                    true,
                 );
             };
             lf
@@ -1380,7 +1381,7 @@ impl SQLContext {
             } else {
                 let existing_columns: Vec<_> = schema.iter_names().collect();
                 let new_columns: Vec<_> = alias.columns.iter().map(|c| c.value.clone()).collect();
-                Ok(lf.rename(existing_columns, new_columns))
+                Ok(lf.rename(existing_columns, new_columns, true))
             }
         }
     }
diff --git a/crates/polars-sql/src/sql_expr.rs b/crates/polars-sql/src/sql_expr.rs
index 148a7fe5735e..f9caa288cb82 100644
--- a/crates/polars-sql/src/sql_expr.rs
+++ b/crates/polars-sql/src/sql_expr.rs
@@ -263,7 +263,7 @@ impl SQLExprVisitor<'_> {
             let schema_entry = schema.get_at_index(0);
             if let Some((old_name, _)) = schema_entry {
                 let new_name = String::from(old_name.as_str()) + rand_string.as_str();
-                lf = lf.rename([old_name.to_string()], [new_name.clone()]);
+                lf = lf.rename([old_name.to_string()], [new_name.clone()], true);
                 return Ok(Expr::SubPlan(
                     SpecialEq::new(Arc::new(lf.logical_plan)),
                     vec![new_name],
diff --git a/crates/polars/tests/it/lazy/predicate_queries.rs b/crates/polars/tests/it/lazy/predicate_queries.rs
index 63cccd65aeaa..49460facc118 100644
--- a/crates/polars/tests/it/lazy/predicate_queries.rs
+++ b/crates/polars/tests/it/lazy/predicate_queries.rs
@@ -11,7 +11,7 @@ fn test_predicate_after_renaming() -> PolarsResult<()> {
         "bar" => [3, 2, 1]
     ]?
     .lazy()
-    .rename(["foo", "bar"], ["foo2", "bar2"])
+    .rename(["foo", "bar"], ["foo2", "bar2"], true)
     .filter(col("foo2").eq(col("bar2")))
     .collect()?;
 
diff --git a/crates/polars/tests/it/lazy/projection_queries.rs b/crates/polars/tests/it/lazy/projection_queries.rs
index 03b7a44bc114..e5870e81ce4e 100644
--- a/crates/polars/tests/it/lazy/projection_queries.rs
+++ b/crates/polars/tests/it/lazy/projection_queries.rs
@@ -22,7 +22,7 @@ fn test_swap_rename() -> PolarsResult<()> {
         "b" => [2],
     ]?
     .lazy()
-    .rename(["a", "b"], ["b", "a"])
+    .rename(["a", "b"], ["b", "a"], true)
     .collect()?;
 
     let expected = df![
diff --git a/py-polars/polars/dataframe/frame.py b/py-polars/polars/dataframe/frame.py
index 911d057a1f46..da79a0cf57df 100644
--- a/py-polars/polars/dataframe/frame.py
+++ b/py-polars/polars/dataframe/frame.py
@@ -4479,7 +4479,9 @@ def reverse(self) -> DataFrame:
         """
         return self.select(F.col("*").reverse())
 
-    def rename(self, mapping: dict[str, str] | Callable[[str], str]) -> DataFrame:
+    def rename(
+        self, mapping: dict[str, str] | Callable[[str], str], *, strict: bool = True
+    ) -> DataFrame:
         """
         Rename column names.
 
@@ -4488,6 +4490,10 @@ def rename(self, mapping: dict[str, str] | Callable[[str], str]) -> DataFrame:
         mapping
             Key value pairs that map from old name to new name, or a function
             that takes the old name as input and returns the new name.
+        strict
+            Validate that all column names exist in the current schema,
+            and throw an exception if any do not. (Note that this parameter
+            is a no-op when passing a function to `mapping`).
 
         Examples
         --------
@@ -4517,7 +4523,7 @@ def rename(self, mapping: dict[str, str] | Callable[[str], str]) -> DataFrame:
         │ 3   ┆ 8   ┆ c   │
         └─────┴─────┴─────┘
         """
-        return self.lazy().rename(mapping).collect(_eager=True)
+        return self.lazy().rename(mapping, strict=strict).collect(_eager=True)
 
     def insert_column(self, index: int, column: Series) -> DataFrame:
         """
@@ -7475,8 +7481,8 @@ def drop(
             Names of the columns that should be removed from the dataframe.
             Accepts column selector input.
         strict
-            Validate that all column names exist in the schema and throw an
-            exception if a column name does not exist in the schema.
+            Validate that all column names exist in the current schema,
+            and throw an exception if any do not.
 
         Examples
         --------
diff --git a/py-polars/polars/lazyframe/frame.py b/py-polars/polars/lazyframe/frame.py
index 9e65f918d385..7aa9a870b9c6 100644
--- a/py-polars/polars/lazyframe/frame.py
+++ b/py-polars/polars/lazyframe/frame.py
@@ -4973,8 +4973,8 @@ def drop(
             Names of the columns that should be removed from the dataframe.
             Accepts column selector input.
         strict
-            Validate that all column names exist in the schema and throw an
-            exception if a column name does not exist in the schema.
+            Validate that all column names exist in the current schema,
+            and throw an exception if any do not.
 
         Examples
         --------
@@ -5031,7 +5031,9 @@ def drop(
         drop_cols = parse_into_list_of_expressions(*columns)
         return self._from_pyldf(self._ldf.drop(drop_cols, strict=strict))
 
-    def rename(self, mapping: dict[str, str] | Callable[[str], str]) -> LazyFrame:
+    def rename(
+        self, mapping: dict[str, str] | Callable[[str], str], *, strict: bool = True
+    ) -> LazyFrame:
         """
         Rename column names.
 
@@ -5040,6 +5042,10 @@ def rename(self, mapping: dict[str, str] | Callable[[str], str]) -> LazyFrame:
         mapping
             Key value pairs that map from old name to new name, or a function
             that takes the old name as input and returns the new name.
+        strict
+            Validate that all column names exist in the current schema,
+            and throw an exception if any do not. (Note that this parameter
+            is a no-op when passing a function to `mapping`).
 
         Notes
         -----
@@ -5083,7 +5089,7 @@ def rename(self, mapping: dict[str, str] | Callable[[str], str]) -> LazyFrame:
         else:
             existing = list(mapping.keys())
             new = list(mapping.values())
-            return self._from_pyldf(self._ldf.rename(existing, new))
+            return self._from_pyldf(self._ldf.rename(existing, new, strict))
 
     def reverse(self) -> LazyFrame:
         """
diff --git a/py-polars/tests/unit/lazyframe/test_rename.py b/py-polars/tests/unit/lazyframe/test_rename.py
index 15eae7d4cc34..45e2d26ac7ca 100644
--- a/py-polars/tests/unit/lazyframe/test_rename.py
+++ b/py-polars/tests/unit/lazyframe/test_rename.py
@@ -1,11 +1,22 @@
+import pytest
+
 import polars as pl
+from polars.exceptions import ColumnNotFoundError
 
 
 def test_lazy_rename() -> None:
-    df = pl.DataFrame({"x": [1], "y": [2]})
+    lf = pl.LazyFrame({"x": [1], "y": [2]})
+
+    result = lf.rename({"y": "x", "x": "y"}).select(["x", "y"]).collect()
+    assert result.to_dict(as_series=False) == {"x": [2], "y": [1]}
+
+    # the `strict` param controls whether we fail on columns not found in the frame
+    remap_colnames = {"b": "a", "y": "x", "a": "b", "x": "y"}
+    with pytest.raises(ColumnNotFoundError, match="'b' is invalid"):
+        lf.rename(remap_colnames).collect()
 
-    result = df.lazy().rename({"y": "x", "x": "y"}).select(["x", "y"])
-    assert result.collect().to_dict(as_series=False) == {"x": [2], "y": [1]}
+    result = lf.rename(remap_colnames, strict=False).collect()
+    assert result.to_dict(as_series=False) == {"x": [2], "y": [1]}
 
 
 def test_remove_redundant_mapping_4668() -> None:
diff --git a/py-polars/tests/unit/test_projections.py b/py-polars/tests/unit/test_projections.py
index 7c279648fa1c..48b3077423e0 100644
--- a/py-polars/tests/unit/test_projections.py
+++ b/py-polars/tests/unit/test_projections.py
@@ -360,9 +360,17 @@ def test_projection_join_names_9955() -> None:
 
 def test_projection_rename_10595() -> None:
     lf = pl.LazyFrame(schema={"a": pl.Float32, "b": pl.Float32})
+
     result = lf.select("a", "b").rename({"b": "a", "a": "b"}).select("a")
     assert result.collect().schema == {"a": pl.Float32}
 
+    result = (
+        lf.select("a", "b")
+        .rename({"c": "d", "b": "a", "d": "c", "a": "b"}, strict=False)
+        .select("a")
+    )
+    assert result.collect().schema == {"a": pl.Float32}
+
 
 def test_projection_count_11841() -> None:
     pl.LazyFrame({"x": 1}).select(records=pl.len()).select(