Russ is a commonly used nickname for "Russell."
Dawg is a slang term for a friend or a fellow. It is often used to address a man or a boy in an informal way.
In combintion "Russ dawg" is a greeting that says hello, signifies commaraderie, and establishes friendship.
"Look it's Russ Dawg! What's up my man!"
"Did you see Russ Dawg out on the town last night? What a legend!"