@JGoldman10,
Snoop Dogg's "doggness" and his becoming really a dog in "What's My Name" is primarily a respect of the music of George Clinton, regarding his iconic song entitled "Atomic Dog." "What's My Name" was Snoop Dogg's debut video, and in this very song, samples are used from "Atomic Dog." With his gesture Snoop expressed the fact that his music has strong roots in the music of Clinton and his companions. And not only his, Snoop's music, he expressed a general thing, the fact that in the 90's many other rappers used George Clinton, Funkadelic, Parliament samples in his songs. Actually, that music was a goldmine for them, they regarded it as a legacy. Also, a George Clinton album came in 1996, which had come into being with the co-operation of many famous rappers, like Ice Cube, Q-Tip, Coolio, Busta Rhymes. However, you can't determine what kind of dog the Atomic Dog is. And "dogs of the world" is heard in the song. So it is a question of disposition, temperament that what kind of dog are chosen as a "totem animal" by a rapper.