Assuming the following:

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

   project = PROJECT
   

1. 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
Edit the filters to update the project or issue type names

OR

Just noting here that you can save a filter that refers to a project by its ID rather than its name. If you do this, the saved filter will not be broken if you change the project's name.

To find all your projects' IDs, go to https://<your site name>.atlassian.net/rest/api/3/project/search

In the following example the id of my project is 10084:

To use it in a filter's JQL you need to type project = 10084

After changing the project's name, the saved filter referring to the project's ID continues to work:

Whereas the saved filter that referred to the project name has broken: