Once you change your name you should re-do any legal paperwork you have so that it's updated with your current name. So even if you were to hold off on changing your name until after the lease signing, you'd still have to go update it and you'd run into the same issue.
What are the legal protections for trans people in your state? For your county/city? Are there non-discrimination laws in place?
What I did when I had to renew my lease was just cross out my old name, write in my new name and attach a copy of the name change order from the court. My complex has an overnight drop box for notices or rent payments, so we just put it in an envelope and left it in there. No issues. I don't think where I live currently has any legal protections for trans people, but I'm not sure. Either way, I had no problems the way I did it.
If you have a personal relationship with your landlord it would probably be best to be up front about it. If you go that route, I would take at least one of your roommates with you for that discussion so that if she doesn't take it well, you have one witness who understands what occurred.
Also know that any time you sign any kind of paperwork for the first year or so after your name change, if anyone does a background or credit check on you, the old name will pop up. So this may be a discussion that you'd be having with any landlord. Not necessarily something you can avoid.