Can I extend my DTV for Muay Thai if I've moved from Samui to Bangkok?

If you’re actually extending at immigration then you’ll have to produce up to date documents showing you’re still engaged in a soft power activity and if you provide them with documents from a gym in Samui then they may decline to process the extension or deny it.

If you are simply flying out and back then there’s a low chance that you’ll be asked to provide up to date documentation upon entry. Most people are simply stamped in.