No, he's not named after the drink or the magazine. Nor is he named after Kramer, because then he would be Kosmo. Although I don't mind that so much, because he's a spaz. But, he is just Cosmo.
Right now he is spending all of his time sleeping, playing, and eating. He's adjusting well to his new home. A particularly poignant moment for me was when he spent 10 minutes sniffing every inch of Kuma's dog bed, which hasn't budged from its position next to my bed. He just wanted to know whose smell was on his new turf. :-)