Then he was hopelessly uninformed. They are allowed under Japanese law, and a quick check show that they can override the standard distribution of assets, where a certain percentage goes to the surviving spouse, less to ligitimate children and even less to illigitimate children.
My parents were never married, but were still an “item” when I was born. They made a deal while my mom was still pregnant, that if I was a girl, she names me and I get her last name. If I was a boy, my dad would name me and I’d get his last name. I got my mother’s maiden name and a Finnish first name to match.
He’s pretty much Whitey McWhiterson. We have a membership card at my store, where you can look up people by their names, and he’s “Dang” in there, but all the other Dangs are obviously Vietnames, like “Quy Dang” and such.
Dang right they are!
As we can see, the law in different places varies a lot. As for convention, hell, wasn’t that what I was bucking all those years? 
My late DH and I never legally married and produced 2 children. They have both our last names, though technically, HIS name is their LAST name. No hyphen (tho’ I think on one birth certificate it was written with one, but not at my request)
I figure they will mostly use his last name (and that’s pretty true of my 16 yr old).
Honestly, we were more comcerned with the first and middle names and just tacked on both last names without a great deal of thought. Not as if the child has to use both.