If there is a mortgage over the property, your lender will need to consent. If someone is being removed from the property ownership and from the mortgage, the lender will need to be assured that you can manage the loan on your own and they will only consent to the transfer if they are satisfied on this point.
If you will be adding someone to the title of the property, that person will also take on the mortgage and the lender will vet them in the usual way and send out a mortgage agreement for them to sign.