Just out of curiosity, do all parts in your system share a family name, have they their own last names, or do they just have first names?
In our system everyone has a whole name, including last one. We don't think we are relatives to each other and having just first name doesn't feel like enough. Since our background stories are different, it's clear everyone has their own last names as well. But names are changeable, like almost everything is, since they are just part of stories.
Inside Fourteen's system many have only first names or they don't have actual human name at all, but something to describe them. Their body has first and last name, like all main parts. I call him Fourteen in here, but it's not how we call him in everyday life. We call him by his body name because that's what we got used to. Name Fourteen came to use because he was going thru a changing process when I started first writing in here, and I didn't know if he was gonna change his name. He didn't in the end, but nobody in their system thinks their body name as their (any parts') own, so it's more like a system name. And since nobody uses it as their own name, Fourteen is as good system name for them than any else name would be. They are not keen on sharing their names anyway, only Leon was fully OK with that, and now even he isn't called that anymore.