A well-known New Zealand entertainer must be running the airline folk ragged. His real name is Allen Stevenson, which is what is on his passport, which also contains the line: "also known as STEVE ALLEN". I wonder which one he books his flights under, as in NZ is is known as Steve Allen. (It goes back a bit, but he sang the theme song for the 1974 Commonwealth Games, "Join Together").
He's just one character I know whose 'known name' differs substantially from his 'legal' name. Another is so well known by a certain name that if he used his legal name, there's a strong possibility that Customs would pull him aside fearing a fake passport.
I guess we have to follow the rules set by the owners/operators of the service, but they sometimes don't make it easy on themselves. I have seen instances where the request is "Surname?", "First nameS?". As already posted above, OK if you're dealing with your own native naming system, but real messy if you're not.
"If in doubt, ask" maybe?
Le Vieux