I got caught on the first name/last name also booking directly on MH website last year. Having mainly done online bookings on QF, VA I was used to inputting first name first, but MH requires surname first. Realised mistake when ticket issued after payment process. I rang MH straight away hoping they would simply fix it - but no, I had to email a certain area, with a copy of the passport and then after several days of no response was told a MYR150 fee was payable to rectify the issue - this was a domestic ticket where the airfare was probably only about MYR330. Argued that I pointed it out straight away and it could have been easily changed - but to no avail (certainly QF would change pretty much anything in the first 24 hours for no fee).
Paid the fee and the ticket was reissued. The domestic leg was connecting to an international flight (separate ticket) so didnt want any issues at check in with name around the wrong way so thought best to get it fixed...