This topic comes up a lot and several people reported rejections on eVisas thru thai consulates (all over the world) when they got that question wrong.
I honestly don't know what the correct answer is but hopefully someone will weigh in about it
SO it's just like with any visa/extension/re-entry, get the new passport in your country, come back, present both passports when you stamp in. They'll stamp you in on the new one, then you go to LTR office and get the visa/re-entry stamp moved to the new passport