His problem is not related to using the Rename Identifier dialog, which was developed specifically to *avoid* the problem you mention. Rename Identifier carefully synchronises renaming across all affected parts of a project. If you find it does not, this is a bug which you should report with a compileable example.
I put example in the attachment.
On the form there is a button named Button1 (both in unit1.pas and in Object inspector). In the OnCreate event of the form there is
Button1.Click; statement.
Now, try to rename Button1 using F2 shortcut (e.g. to ButtonTest). It is renamed in unit1.pas, but not in unit1.lfm (and consequently in Object inspector).
When you try to run project now you get access violation error:
[Window Title]
Error
[Content]
Project project1 raised exception class 'External: ACCESS VIOLATION' with message:
Access violation reading from address $0000000000000000.
In file 'unit1.pas' at line 34:
ButtonTest.Click;
If you can confirm that this should not happen, I'll report bug.
I tested this with Lazarus 2.2.0, FPC 3.2.2, Windows 11, but it is exactly the same with Lazarus 2.0.10.