Is there a database of all known star names/identifiers?
The closest service to what you are describing is the SIMBAD Astronomical Database from the Université de Strasbourg/CNRS. At the time I write this post, it contains 10.8M objects and 35.5M identifiers. It does not have a single CSV you can download with this information (to the best of my knowledge, and I've asked), but there is an API and TAP service available for programmatic access.