At a closing the other party lawyer put my name on mortgage but not on deed

So where was YOUR lawyer at the closing?
Yes, you can sue, of course. But you don't tell us anything - are you 2 private individuals? Two corporate entities? What is your relationship to the 'other party?' Have you told this other party to march on down to city hall and add your name to the deed, for a small filing fee and no revenue stamp fee (when no money is changing hands)? Did you contribute to the down payment? Are you withholding your half of the mortgage payment in a lawyer's escrow for now? I'm guessing not. We need more help from you.

I agree, where was YOUR closing lawyer... and please don't tell us you were to cheap to hire one. A house is the biggest and most expensive purchase / investment most people will ever make.

So who's name is on the deed? When was the closing? When did you discover this? What have you done to correct this? There are so many questions that need answering before we can give you proper advice.

And if the lawyer failed to put OP's name on the deed, OP should have objected then. As others have noted, OP should have had an attorney. Failure to be represented by one makes the failure to catch the omission your fault, not the fault
of the other party's attorney.