I work with actors, we do it all the time.
The reservation is made under your real name, then when you check in, you have them put an assumed name in the main area on the system where they would look if someone is calling and trying to get your room via phone.
Your real name is still on the reservation (for those times when you lose your key or have to get one reset), but the "public" assumed name is what they see when looking you up on the system.