Going with the theme, as a kid I used to crack up at scenes from Looney Tunes like this. Daffy is a duck not a rabbit and the general air of stupidity emanating from the creature is comical, especially to a kid. But why? Was there some specific group of people being mocked, or was it just a dumb voice? And how widely used was this accent/voice used for comedic effect?
You are really asking multiple questions. I can answer the one in your post's title, about the voice of the character who says, "I will name him George". The best example is the Abominable Snowman in the Warner Bros. short The Abominable Snow Rabbit (1961), from which your clip is taken. In the 1939 feature film adaptation of John Steinbeck's novel Of Mice and Men (1937), actor Lon Chaney, Jr. (better known nowadays for playing the Wolf Man for Universal Pictures) played the role of Lennie, a lumbering, mentally challenged man who likes to pet rabbits and other soft, furry creatures. Mel Blanc, who made the voices for all the characters in this short (and indeed almost all of the Merrie Melodies and Looney Tunes characters), is imitating Chaney's portrayal of Lennie when he speaks as the Abominable Snowman. George (played by Burgess Meredith) was the name of Lennie's companion/guardian in Of Mice and Men, not of any rabbits in the movie, so obviously director Chuck Jones is not staying entirely true to the Steinbeck character in the cartoon, but simply doing enough so that the older adults in the audience of 1961 would recognize the reference. I don't want to spoil the movie for you if you haven't seen it, and it's absolutely worth seeing, but the violence that the Abominable Snowman commits in the Warner Bros. short has its parallel in the feature film as well (not to mention the novel), and it ultimately becomes rather grim.