diff --git a/pymc/step_methods/compound.py b/pymc/step_methods/compound.py
index d0393afd57..1fcb3d2673 100644
--- a/pymc/step_methods/compound.py
+++ b/pymc/step_methods/compound.py
@@ -22,6 +22,7 @@
 
 from abc import ABC, abstractmethod
 from collections.abc import Iterable, Mapping, Sequence
+from dataclasses import field
 from enum import IntEnum, unique
 from typing import Any
 
@@ -96,6 +97,7 @@ def infer_warn_stats_info(
 
 @dataclass_state
 class StepMethodState(DataClassState):
+    var_names: list[str] = field(metadata={"tensor_name": True, "frozen": True})
     rng: RandomGeneratorState
 
 
diff --git a/pymc/step_methods/state.py b/pymc/step_methods/state.py
index f50aff7e25..ec7bbbae48 100644
--- a/pymc/step_methods/state.py
+++ b/pymc/step_methods/state.py
@@ -67,7 +67,12 @@ def sampling_state(self) -> DataClassState:
         state_class = self._state_class
         kwargs = {}
         for field in fields(state_class):
-            val = getattr(self, field.name, field.default)
+            is_tensor_name = field.metadata.get("tensor_name", False)
+            val: Any
+            if is_tensor_name:
+                val = [var.name for var in getattr(self, "vars")]
+            else:
+                val = getattr(self, field.name, field.default)
             if val is MISSING:
                 raise AttributeError(
                     f"{type(self).__name__!r} object has no attribute {field.name!r}"
@@ -89,11 +94,17 @@ def sampling_state(self, state: DataClassState):
             state, state_class
         ), f"Encountered invalid state class '{state.__class__}'. State must be '{state_class}'"
         for field in fields(state_class):
+            is_tensor_name = field.metadata.get("tensor_name", False)
             state_val = deepcopy(getattr(state, field.name))
             if isinstance(state_val, RandomGeneratorState):
                 state_val = random_generator_from_state(state_val)
-            self_val = getattr(self, field.name)
             is_frozen = field.metadata.get("frozen", False)
+            self_val: Any
+            if is_tensor_name:
+                self_val = [var.name for var in getattr(self, "vars")]
+                assert is_frozen
+            else:
+                self_val = getattr(self, field.name, field.default)
             if is_frozen:
                 if not equal_dataclass_values(state_val, self_val):
                     raise ValueError(