I had this problem on an Air Mauritius booking from JNB to MRU
Booked on their website and didn't realise that their web-form was surname first!
I called up and was told it was not a problem. Calling up and explaining to the agent in MRU was a challenge in itself.
The issue only manifested itself at the airport momentarily when the check-in agent scanned our passports and couldn't find us on the flight. As soon as I mentioned the names were the wrong way round, he found us. Phew! I'd be prepared for that happening, and I'm sure it will be fine.