Used as a component of a nickname, especially in street names and the names of rappers, e.g. Snoop Dogg or Nate Dogg.
"The rapper adopted the stage name Jay-Dogg to fit into the tradition of artists using "dogg" in their nicknames."
Dogg is simply an alternative spelling of the word dog that has been used interchangeably throughout history. It carries no distinct original meaning or separate origin from its standard counterpart.