I've never seen any convention on this. It's best to give a DB a short meaningful name with no spaces. Sometimes DB names may be for example suffixed with '_DEV', '_TEST' etc if you've got development databases on the same server. If you've got a number of DBs with very similar names it can be confusing so avoid this.
What an utterly horrible idea. So when my content_music and content_general databases go into production the system fails miserably because all the testing was done with SPs in content_general_test (whose name is changed to content_general in the release process) referring to tables in content_music_test (whose name is changed to content_music in the release process, so that content_music_test exists only on the test system, not on the production system).
OK, it's not likely to happen, if your release processes are reasonably professional. But I would strongly recommend not giving it the slightest chance to happen, and sticking "_TEST or _DEV or other postfixes on the database name in various stages of design, development, test, system test, pre-release validation, everything before release is just giving this particular failure a chance to happen in production.