The Handicapper General's name is mentioned on the first page, but she is rarely talked about until the end of the story when she walks into the auditorium and shoots Harrison and the ballerina with a double barrel shotgun. The author's use of the name Diana Moon Glampers leads readers to infer through his use of Mythological Allusion that Glampers will kill something. Diana was the goddess of the hunt/chase, she carried a bow and arrow, and her symbol was the moon.
Kurt Vonnegut, Jr. describes the main characters of "Harrison Bergeron" in his usual matter-of-fact and rather sarcastic way, from the perspective of the society that he creates. For example, when we are introduced first to Hazel, Harrison's mother, the first bit of character description that we get of her is that she wasn't very smart, and that
"There were tears on Hazel's cheeks, but she'd forgotten for the moment what they were about."
Immediately we feel like she is a rather shallow person, and a total ditz. Vonnegut is describing her through the eyes of the society that they live in though, not through our eyes. According to the society that existed in this story, in 2081 where everyone was "finally equal," they did find Hazel average and dull. Vonnegut characterizes them according the standards of his dystopian society.
Later, we see Hazel is willing to bend the rules a bit (she encourages George to take off some of his weights, just to rest) but that George is more of a stickler for the rules. The most flamboyant and exaggerated characterizations come in describing Harrison. Here, Vonnegut gets a bit wordy and even poetic. He describes Harrison as all "Halloween and hardware," and later, when Harrison bursts onto the stage, as "a man that would have awed Thor, the god of thunder." Vonnegut uses similes and metaphors and other poetic techniques to describe just how overwhelmingly beautiful and strong Harrison is. This would be true to his society's perspective also, since they were used to average.
I hope that helped a bit; good luck!