Yes, they very much do.

You would not have been on a plane named Bangkok, as that is the English name. HS-TXM (an A320) is named Krung Thep Maha Nakhon, which is the short version in Thai, so that is your Bangkok plane

As for how they decide, I cannot answer - it does seem like the A320 fleet is very much focused on city names (especially secondary cities), presumably to reflect the network they operate.