Adding your wife's name to the title of the caller is a bit different than changing the terms of the loan. You should be able to add your wife's name to the title of the car will without affecting the loan or its terms. But you should look at the terms of the loan to see one requirements there are in notifying the lender.
The above is not legal advice. It is an illustration of options that can be used in certain situations. I have not examined all of your facts, if I did I might provide a different response.