Are there any unwanted side-effects from renaming the DB? For example, renaming a test DB name to a prod DB name?
Should this be as straight-forward as renaming the DB file?
No problem with that. Note that you will have to open the database manually once via Database > Open afterwards.
Just don't duplicate databases without changing their unique ids. See Change Database ID (https://www.photools.com/help/imatch/#rmh_config_database.htm?dl=h-10)