If I buy a motorcycle in BKK then later move to Chang rai what do I have to do with transferring plates. Once in Chang rai will I have to come back to bkk?

You can change the plates if you want at Chiang Rai DLT, they send the book back off to the Bangkok DLT office after you have fill out a couple of forms.

You don't have to change plates you can just get your new address put in the book.

You don't have to change plates. I bought my bike while living in Pattaya and now have been living in Korat for 7 years with no problem on the Pattaya plates.