The name change is explicitly for changing names from inappropriate to appropriate, not for any RP purpose. Any name change requests like that would get rejected out of hand.
If someone else wants to play an offshoot of your family, they should start their own account and RP it as being an offshoot of your family.
Fundamentally, what you're talking about is, in fact, a new family, so there's no good reason that it should be anything other than that mechanically.
What's the purpose of handing over your account to someone, anyway? Just so that they could start with lots of fame? If they kept your characters, it would cause all kinds of confusion and logical problems, and they would be thrown into the middle of everything at a time when they should be trying to learn the game at their own pace.
