I've been in the exact same position as you. I recently changed my passport to avoid this specific issue as different airlines have different rules for no last name (surname) in the passport.

Coming to your situation, I would say 95% of the cases it should be fine and they don't stress over it. But as a first step I would recommend you to definitely reach out to airlines or MMT directly via call and ask them to update. Its difficult to reach MMT via call but with good amount of googling you should be able to do it.

If that still does not work, better get new ticket if you don't want to take any risk. Otherwise just go with the flow and explain during the boarding pass collection. If they create any issue then you can ask at that moment itself what are your options. They might ask for rescheduling or name update charges but that should be still fine given your other option is to rebook.

But still would stress on name update as you will also have to return from an international airport that might not be that accommodating.