This is a reference to the sitcom "Friends" and names the three main male characters on the show. In the context of the song being relegated to this fate of watching a defunct, yuppie-oriented, caucasian program serves to illustrate a pathetic existence
Diamonds are often referred to as "ice" because of their clear, glassy nature and resemblance to ice. His chain (necklace) has so much "ice" in it it's making his neck cold, allegorically speaking.