As I mentioned above, I don’t think this actually addresses the script issue.
First, though, we probably should address the semantics. The name Jawi properly refers to the Arabic script (ISO 15924: Arab) when used to write the Malay language (ISO 639-1: ms). But in Thailand it more often refers to the Pattani dialect of Malay (ISO 639-3: mfa), which is also spoken in Kelantan. I.e. both standard Malay and Pattani Malay can be written using either the Latin alphabet or Arabic (Jawi) script.
Simply using name:en for the Latin script wouldn’t be correct if the place has a Malay language name that is different from English.
So there’re actually two questions here: (1) Should place names in the Pattani Malay dialect use name:ms or name:mfa, and (2) When both Latin and Jawi (Arabic) script are used, how should we distinguish them?