According to a city contract, "Anaheim" must be first in the team name and, notably, the only geographical identifier the team carries.
It's unclear whether or not the Kings would keep that particular moniker, but what is clear is that they will not be the "Los Angeles Kings of Anaheim," "Orange County Kings," "Los Angeles Kings of Anaheim via Sacramento," or what have you (the drama that goes into naming a team).
Apparently the city of Anaheim learned its lesson with the Angels in 2005, when the baseball team changed its name to the Los Angeles Angels of Anaheim in order to tie itself to the bigger market.
The city of Anaheim's contract with the Honda Center (where the NBA team would presumably move) stipulates, "teams scheduling a majority of home games each season in the arena include 'Anaheim' as the first word and as the sole geographic identifier in the name of each team."
Now that the locator is settled, fans are left to speculate what Anaheim's NBA team would be nicknamed. There is some talk among sports fans that the Kings might go back to being called the Royals, the franchise's original name.
Joe and Gavin Maloof, who own the Sacramento Kings, are awaiting approval from the majority of the NBA's owners to officially move the team to Anaheim. Should the move go through, Southern California's newest NBA team will tip off next season.