What is the process for transferring a DTV from an old passport to a new one, and can you enter Thailand with two passports?

there is no process to transfer a DTV sticker 😮

If you got a sticker visa from a consulate) to another passport, you carry BOTH passports to enter/exit the country for the next 5 years the DTV sticker in the old passport is valid for and you'll get stamped in and out on the new passport

Now on the other hand

If you have a PDF file from an eVisa DTV you just copy/print the data page of the old passport and your last entry/exit stamp from thailand on the DTV from that passport

Then you present the PDF print out of the DTV, the copy of the data page and last entry/exit stamp on the old passport along with the new passport when you stamp IN to thailand