I do think they should keep the same family name, a Villainous Player can curse their own family name by his actions, and make the relatives suffer for that.
I do have a disowned character, but i made it IC. My family Disowned my Character on the FEI, she decided to become a Priest, act who is forbidden for a Military Family like mine. So when i talk about "that member" of my family she have less ties than an adventurer, because adventurers...well they still fight.
Families should have a mix of good and bad members, who knows, have you wondered what is heavier..... Fame or Infamy?
peace!