How can I transfer ownership and register my motorbike in Chiang Mai after purchase from Fang District?

Any service centre where you see this sign can do it for you for a small fee.

We bought a car out of province.. the procedure was to attend to the transfer of ownership in the province where we bought it.. ie. the sellers province.. which immediately moves legal ownership into your name.. but since we lived in a neighbouring province they said it was not acceptable (legal) to leave it registered with them.. and they gave us 7-days to get the car re-registered in our own province.. after which we would be fined for non compliance.. when you do this you will have a plate change which will also be reflected in a replacement tax disc.. which means buying a car or bike in another province with a 'very nice' plate is pointless because you won't be allowed to keep it!

You can get an agent to arrange the transfer for you in Fang, and then get re-registered locally

I worked really hard at the transport department and actually got them to send it up there and 3 weeks later it was all done. It was hard to get them out of their comfort zone. I think it cost me 100-200 baht and an hour's time. I bought them a red velvet cake as a second thank you.

go to one of the government inspection sites and they will do it, not expensive

You will need a residence certificate from immigration to register it in your name