If a couple marries how is the new name added to the mortgage?
Congratulations on getting married.
I would first contact your servicer of your mortgage to see if there is a provision on your loan that allows you to add someone to the mortgage due to marriage. There might be some circumvented process to do this direct through the current lender. It's not something that I have heard of but it does not hurt to ask the worst that happens is they say no. Mortgage holders don't allow people that get divorced to just remove a borrower but there is sometimes a process where the spouse can assume the loan if they qualify.
If they say no than you have to refinance the home in order to have another borrower added. Reason is the bank wants to know if that person is a qualified borrower; credit, income, assets, debt, etc
You can have the spouse added to title which I think is what your ultimate goal is. You want to have them on title as a tenant thus giving that person rights to the home. You can go down to the county recorders office and ask to have the Deed that is recorded updated to add an additional person. Go to your local county website and see if any of the forms are online that you can download thus when you get there all that needs to happens is to pay for what it will cost to do it.