Possible to block my phone number but NOT my name?

Don't believe this is possible on the AT&T network.

In a word, no.

With Show My Caller ID on, your name isn't sent with your number anyway, which isn't included with the number when calling from a cell phone.

Your name appears on the recipient's phone only if your name and phone number is available in the recipient's address book on their phone.

CallerID on all networks across the known universe is handled locally on each network.

Each carrier, when they receive a call, checks their own database of names and if they get a match on the inbound callerID, they display the name.

The "big guys" hand off name/phone databases in the background through secure channels (no small companies and certainly no individuals).

So, when you see a "Name" on your callerid screen, it is because that name matched up to the callerid NUMBER that was sent. Without the number, there can be no name to match up on the local database.

I build VOIP Telephone systems for a living. We can broadcast (literally) any phone number/name we want when making a call. The name is ignored. The number, however is what appears on the CallerID screen. If that number matches with a name in your provider's name/number database (acquired from their provider or one of the big companies), the name will appear instead ... IF you have paid for name service.