I actually was thinking that "Caesar" would be the title, Hosue would be the family name.Then how about the ruling family of the Vegan Empire ruling out of Caesar's Palace and calling themselves Caesars? I still like the idea that the first Caesar being named Randall because it makes it clear that his dynasty was started by random charismatic man. The image of an Ozymandian monument amongst the ruins is too good not to include.
Plus there could be a cult worshiping a goddess they call "Lady Luck". The fall of Vegas would ironically strengthen the cult since they'd see it as Lady Luck striking down the Vegans for trying to "cheat the system" or something.
What about Randall House?