You can use any name as long as it is unique to you and no one else has it. Again, you need to register as both a writer and publisher. Here is my ASCAP information:

WRITER: Douglas Showalter
PUBLISHER: The General Public (ASCAP)

They are both separate costs, and add up I think to around $50 for the two. It is well worth it to do both. They do ask for your TAX ID number, SSN, etc. I don't have a Tax ID number and I am a member. If you are going to start a business regarding your music, it wouldn't hurt to have them correlate. I think that is on you honestly. You can call it what you wish to my understanding, again pending that no one else has that name.

Hopefully this helps. You can always call ASCAP and patiently wait for them to answer your questions.