fix(NOTIFY-1166): only fire callback when account name has changed (#…

…4735)

## Explanation

This PR ensures the `onAccountNameUpdated` callback only fires when the
new name is different from the previous one

## References


[NOTIFY-1166](https://consensyssoftware.atlassian.net/browse/NOTIFY-1166)

## Changelog

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### `@metamask/profile-sync-controller`

- **FIXED**: `onAccountNameUpdated` will now fire only when the new name
is different from the previous one

## Checklist

- [x] I've updated the test suite for new or updated code as appropriate
- [x] I've updated documentation (JSDoc, Markdown, etc.) for new or
updated code as appropriate
- [x] I've highlighted breaking changes using the "BREAKING" category
above as appropriate
- [x] I've prepared draft pull requests for clients and consumer
packages to resolve any breaking changes


[NOTIFY-1166]:
https://consensyssoftware.atlassian.net/browse/NOTIFY-1166?atlOrigin=eyJpIjoiNWRkNTljNzYxNjVmNDY3MDlhMDU5Y2ZhYzA5YTRkZjUiLCJwIjoiZ2l0aHViLWNvbS1KU1cifQ

packages/profile-sync-controller/src/controllers/user-storage/UserStorageController.ts

@@ -896,7 +896,12 @@ export default class UserStorageController extends BaseController<
             },
           );
 
-          this.#config?.accountSyncing?.onAccountNameUpdated?.(profileId);
+          const areInternalAndUserStorageAccountNamesEqual =
+            internalAccount.metadata.name === userStorageAccount.n;
+
+          if (!areInternalAndUserStorageAccountNamesEqual) {
+            this.#config?.accountSyncing?.onAccountNameUpdated?.(profileId);
+          }
 
           continue;
         } else if (internalAccount.metadata.nameLastUpdatedAt !== undefined) {