We took our first 5th into Mexico a few years ago - registered to husband - didn't return the permit - and then sold it in Canada. We now have a different 5th, and are returning to Mexico in January ...
TIPS are issued via PASSPORT NUMBER. Use the other name. No hassles. As long as the motor vehicle registration has the name of the permit requester on it, it will be no problemo. The RV should be in both names, use your name, your passport number, you valid driver license to get the new permit. No guesswork about this.