I've never heard of anyone doing their legal name change before going full-time. And you're taking it a step further and doing your name change before even going part-time?
I have to agree with JanePeterson. Transitioning is a very long process (especially the social aspect). And attempting to do it all overnight is just... it might be too much to handle emotionally. I'm worried about you. Is your therapist on-board with this plan?