I think I ran into you on Twitter didn't I (@pux0r3)?
It's definitely a good strategy. You'll probably want to give each userid generated via Firebase Authentication a "display name" field in your database with this name. Just looking around at different games services I'm on, Battle.net does add a #<random digits> to my username and Stadia has a similar feature for new users.
You'll want to be careful about your database structure to make sure that the process by which you add these annotations is fast and guarantees uniqueness (it would be easy to lock up your entire database if you did some exhaustive search over your entire `users` node to perform this action).
--Patrick