Yes, we do use different names for different sites because we have different personalities for all of them. On some I am a sub and on others he is. Different sites seem to do better with certain personalities.
Like luv2b_watched, I only model on one site, so I only have one modeling name. If I were to branch out into other sites, I think I would use different names for the different sites. Customers could still follow you from one site to another; you would just have to tell them your name on the new site(s).
I have two different sites that I model from and I have a different username for each site. Personally, I like the variety of having different usernames and different personalities on each site. On one, I can be more domineering, while on the other, I can be more submissive. I feel like it gives me more leeway to cater to client’s fantasies.