What does the name of Diana Moon Glampers suggest?

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.
https://literarydevices.net/allusion/