I really don't mind my hyphenated surname (born with it, not changed by marriage). For airlines I have been putting in the last name without the hyphen or a space since as long as I have been booking travel tickets. I have never had an issue with a check in agent or similar understanding ticket name and passport name are the same, just a hyphen missing from one.

With multi part (no hyphens) surnames it is the same idea, no spaces, mush it together - it is hugely common in some parts of the world to have multi part names, e.g. Van Dyke, van der Lann, etc etc. so any other two word surname, no hyphen, would work the same re travel bookings.