This is sort of a weird one. While I was testing ways to re-populate a neighborhood made empty by the plague (aka the Mac file limit), I experimented with creating a 1-person family, moving them into an "abandoned" house, and then using the SimBlender to teleport the vanished sims who used to live there in from the Default Family ether. That didn't work, and I just recreated the family in CAS, and moved them onto the lot. Then I moved my placeholder Sim out, which unfortunately left the lot with his last name on it. I tried moving the family out (after ensuring that their belongings would stay put), and then back in, but the family still retains the name of the placeholder Sim (Ufen) even though their actual last name is Hopper.
So, it doesn't affect anything really, and I don't mean to sound whiny, but is there in fact anything I can do about this? I don't have SimPE; my operating system is too old for the Mac version that recently came out.

Just have someone with the last name you want move out on their own using the Find Own Place option, move them into the lot where you want the family to live, and then move the rest of the family in with them.

Well, they're already living there, so I suppose I'd have to move them all out, and then back in. But you're saying do it with the computer, not from the Neighborhood view, yes?

Yes, just move the one person out with the computer, that will create a new family with the new name. Then move everyone else into that family.