Hi yank, and welcome to the forum!
In Thailand, people change their names quite often. It doesn't have to be anything to do with marriage.
Having said that, it is quite often done (especially when changing a Thai surname to a foreign one) during the process of legally registering the marriage.
In answer to your question, he can't change her last name, she has to do it. So, what he must do, if it's really important that his ex changes her surname, is that he must contact her and ask her to do it.
In the eyes of the law, people who do not register their marriage with the Thai authorities, are not married.
If, by some kind of accident (possibly a person not really understanding what was going on?) the marriage is actually registered in Thailand, then he would need to get a divorce. This can be quite straight forward if both parties are in agreement, but again would involve him getting in contact with her.
What I would suggest, is that you try and find out how the name change was done. Ask your fiance how his ex went about changing her name, what processes did she go through?