Kramer was called "Kessler" because the real Kramer (Kenny Kramer, not Michael Richards) did not want his name to be in the show. After the pilot, Jerry said to Larry that the name had to be Kramer, because it just sounded funnier, so after a lot of work it finally became Kramer.
The coffee shop in which Jerry and George are was not intended to be implied [by viewers] as "Monk's". It has been said that Monk's and Pete's are two totally different shops. That explains why we never see the waitress, Claire, again. (Taken from "Notes About Nothing")
The character of Elaine was not cast as of this episode. After the pilot NBC said to Jerry and Larry that they could make four more episodes, but only if they bring in a female character into the cast.