There's no reason a child can't have two middle names. If you don't believe me, take it up with George Herbert Walker Bush.
Or Prince Charles, who has three middle names.
My father has two middle names. My brother has two middle names. Why is the concept so upsetting to you, Dis?
But poor Bonnie Prince Charlie has no last name. I don't know what they do in the U.K. when you have a House instead of a surname....
Anything they want...
I'm still looking for where the OP said anything about a hyphen.
Since she specifically referenced middle names, and since middle names are rarely if ever hyphenated, it seems like a great deal of fuss for something that is likely not even relevant.
(And honestly, best interest only really becomes an issue when there's an objecting party - in the case of two parents in agreement, it's rarely raised as an issue unless the name is particularly obnoxious or offensive. Heck, the judges rarely even look that far if there are two parental sigs on the form!)