What should I do when reentering Thailand with a new passport while holding a DTV visa?

Not yet, but noted on both of my children's visas that the passport will expire soon (they are 5 year only). Full validity of the visa given, so one might presume they expect you'll need to enter with both old and new passports in future. I gather if a passport is lost, one might also need a photo of the old.

Yes that's the best thing to do .

My wife always take her old passport with UK visa and new passport when rentering the UK .

Bring both passports and a printout of your Evisa