I rarely need to work with the AX database. In my company developers work on the AOS, and leave SQL related thing to the BI and installation people. Therefore, if I want to see the name of the database that an AX installation uses, it means I am either doing something I should not be doing, or are really desperate..
..and then I can never find the form where you can see the name of the database!
For future references (and to shorten those moments when you are not sure if you restored the correct database), to see the name of the database that contains the data, go to:
System Administration > Inquiries > Database > Database information
If you are a hardcore developer who prefer to dazzle others with your AOT skills, you can find this form at AOT > Forms >