I think it's really unlikely that any transgender support place would expect you to change your name and gender before you go there. One of the major missions of such places is to help people just like you, who are in the beginning stages of transition or trying to figure out what's right for them. It would pretty much defeat that purpose if you had to make up your mind before going.
They may not even care if you use your legal name; I've been to places that offered free therapy, and some of them were OK with giving them another name. The people who run such places understand that this is scary stuff for many of us, and being anonymous can be a big help when we're starting out.
You'd have to give your legal name if you were signing up at a regular clinic for therapy or medical services, but even there, any place you'd want to go should routinely ask you for your preferred name and pronouns. That's just basic courtesy.