Do I need to update my Thai visa when re-entering with a renewed passport?

Yes, you show both passports. Your visa has a passport number on it, so they want to see the passport that corresponds with your visa. But then since that passport is no longer valid, they will put your entry stamp into the new passport.

You don't need to do anything besides check to make sure you got the correct stamp before you leave the airport. Continue to carry both passports for the remainder of your DTV and you shouldn't have any issues.

Some immigration offices might be willing to put a notation in your new passport that references your old passport number, but even with that it's not a guarantee for entry. The only sure way is to keep both passports.

They should transfer your stamp to the new passport on re-entry