It's a funny thing but I would say the answer is yes.

or 2 names as in 2 totally separate identities?

I have first and last and my rate is the average rate.

the rates or the two names.
I say the rates came first, and then the name.

Generally, in my experience, ladies that intend on being High Dollar, extended appointment ladies make that choice first, and then name them selves accordingly which is to have two names.

I recently met a lady that will become an "HDH"; because that is the market she is wanting to appeal to when coming up with her stage name she specifically wanted to have two names (first and last) as that is the expected naming convention for that market.

There are ladies that happen to have two names and don't charge more, but ladies that charge more almost always have two names.