Welcome to the Club. The MH Page is not very clear about that as they state on Name and Surname instead of Name and Given Name or First Name.
I have to recent experiences:
A friend flew with wrong names on MH without problems. Had contacted BAEC on twtter to get the flights credited though, as the BP does not match his OW Emerald status thought.
I myself have had the same problem of mixed first and last name. Contacted them and was told it should be fine. Check In will correct it. But I decdied to play save and used the opportunity while transiting in KUL last week to get the ticket correct for a nominal fee or app. 55 EUR - just to be on the safe side, as I will start my trip with this ticket in February from TPE and the check in staff there is from CI and usually not very good in dealing with anyhting not regular.
For further information have a look at
https://mhcare.malaysiaairlines.com/...language=en_US. They are also very attentive on Facebook messengers