What does the name Diana Moon Glampers suggest in "Harrison Bergeron"?

The name "Diana Moon Glampers" is full of allusion and allows a great deal of interpretation that can enrich the meaning of Vonnegut's "Harrison Bergeron." 

First, the name as a whole sounds funny and presents a stark contrast within itself. Diana is a lovely, flowing name that means heavenly, divine, or perfect. But Glampers is a clumsy, ordinary, even ugly name. The contrast corresponds to the society the Handicapper General works for; it is ostensibly perfect because all people are finally equal. In reality, it is a very ugly society that removes everything beautiful its citizens are capable of. The wry humor of the name is menacing in the way that the final joke of the story is more sickening than cheering.

The name Diana is an allusion to the ancient Roman goddess of the moon and the hunt. Diana Moon Glampers is a goddess in the sense that she has supreme power over the subjects of the United States in 2081. She also proves to be an excellent hunter when she takes down Harrison and the ballerina with her "double-barreled ten-gauge shotgun." 

The use of "Moon" as the character's middle name also allows some interpretation. Because the middle name repeats the idea of the first name in a "dumbed down" version, it represents the dumbing down of the society in order to ensure equality. To moon can also have the meaning, as a verb, of pining after someone or something sentimentally. This would be ironic if applied to the Handicapper General because she is anything but sentimental. It could refer to the idea that the society aimed high--aimed for the moon, so to speak--in wanting to create an equal society. 

Finally, Glampers may call to mind the word "clamper." Diana Moon Glampers is the one who must clamp down on those who violate the laws of equality. Because of its inelegant sound, it sounds like someone who runs roughshod over the feelings and rights of others. 

One can read many things into the simple name chosen by Vonnegut for the Handicapper General: Diana Moon Glampers.

Diana Moon Glampers is the Handicapper General of a future, dystopic United States in which everyone is forced to wear handicapping devices so that nobody can be better than anyone else. She is a symbol of a mindless bureaucracy that will do anything to maintain its power, especially by way of unnecessary violence.

In this society in which "everybody [is] finally equal," excellence is suppressed, following the idea that true equality is achieved when no individual has unique attributes that may outshine another's abilities, making them feel inferior. No person can be more beautiful, more intelligent, or more competent than another. Harrison rebels against such suppression, and in response, Glampers, whose name sounds like "clamper," clamps down. As Harrison and a ballerina dance in an "explosion of joy and grace," having shed their handicapping devices, she enters the television studio with a ten-gauge shotgun. She shoots and kills both of them.

Glampers doesn't even try to understand what Harrison's protest is all about. She simply uses the legally sanctioned violence of the state to destroy him. Not being described as bearing any handicapping devices herself, it's clear that Glampers naturally has no impressive or individualistic traits that would mark her as anything beyond "average." She is a symbol of the mediocrity that rises to the top when mediocrity is the highest social value. Her narrow-mindedness and total control blocks her society from doing the thinking and soul-searching it needs to course correct, and when a citizen attempts to reflect even on the simplest of things, their handicapping device makes it impossible for them to come to any real or meaningful conclusion. Harrison's father, George, wears a mental handicap radio that emits a deafening sound about every twenty seconds, keeping his above-average intelligent thoughts at bay.

Glampers and the society that exists in 2081 warn against the dangers of repressing individuality and confusing conformity with equality. With no person being allowed to excel and effect change, the society will remain stagnant and eventually crumble.

What are Diana Moon Glampers' traits in "Harrison Bergeron"?

We aren't actually told that much about this character in this excellent short story. She only appears for two paragraphs, but in those two paragraphs she definitely manages to make an impression and leave her mark! Consider what we are told about her:

It was then that Diana Moon Glampers, the Handicapper General, came into the studio with a double-barreled ten-gauge shotgun. She fired twice, and the Emperor and the Empress were dead before they hit the floor.

Diana Moon Glampers loaded the gun again. She aimed it at the musicians and told them they had ten seconds to get their handicaps back on.

It is at this stage that the television screen goes blank, so no more is seen by the Bergerons. However, we can see from Diana Moon Glamper's brief role that she is definitely a force to be reckoned with. She is ruthless and violent in the way that she shoots Harrison Bergeron and his Empress, she is also threatening in her attitude towards the musicians and clearly feels she has power.