Does my name have to be on the mortgage to be on the deed?

No Yes and Maybe, it will depend on the mortgage agreement ( their terms) and also how you wish to have your name added. If it is being added "in commom" it should not be an issue, but you can't of course have a share ownership that would attempt to take that share of ownership out from under the mortgage.

So you will have to work with a real estate attorney to review your mortgage and type of deed you have.