No issue with flying if your first/last name is jumbled. As long as it's the same name per your identification, the sequence doesn't matter to MH.
Getting it credited to FFP however is the problem. If you've put in a FFP number, you may not be able to OLCI until you've removed the FFP number as there is a name mis-match.
I would call MH and see if they can rectify it for free beforehand. If they don't, the check-in agent might be able to help on the day.