Assuming the following:

1. I have a project named PROJECT with key PROJ
2. I create a filter:

   project = PROJECT
   

3. If I rename PROJECT to NEWPROJECT then the field produces
   

Suggestion:
Is it possible to bind the search to the project key or issue type ID instead? That way, renaming a project should leave filters unaffected.

Workaround

1. Look for all filters using the old project name in the database

   select * from searchrequest where reqcontent like '%PROJECT%';

2. Edit the filters to update the project or issue type names