Sort of. It's a family name, so it's passed down from parents to show who's related to who, but we don't usually pass down given names in my time.

[Though Ren is never one to talk about his family much.] Though which order you introduce yourself in depends on what part of the world you come from, too. I'm used to family name before given name, which is why I said it that way, but a lot of other countries use given name, then family name, so that would be Ren Suzugamori in my case.