It covers everything. That will be what the office admins will call you when they talk to you, the name they'll book your appointments under, etc. Telling them that's not your name and that you're going by a different name doesn't make any difference. Only place I've been so far that doesn't respect preferred name, especially a legal one.
The actual psychiatrists aren't too bad once you tell them the right name, it's just the front desk.
Basically just a warning that if you go there without all your paperwork 100% changed you WILL get deadnamed repeatedly.