I’ve always had a odd feeling this character name is in reference to someone possibly from a political issue at the time the story was written, this is the only character where the middle name is included in the story.
But all I can find is that it is possibly the goddess Diana, which doesn’t make much sense.
If anything, it’s likely just a reference to other Vonnegut stories. Another character named Diana Moon Glampers later appears in God Bless You, Mister Rosewater. Vonnegut often reused characters (or at least their names) in his various books.
Note that Diana is the Roman goddess of the Moon. The virgin goddess, that is.
One might guess that she’s the child of some flower-children type parents and rebelled against that, becoming an extreme conformist/prude
She has a bit bigger role in the TV movie Between Time and Timbuktu which has the Bergeron story as as subplot. In fact, Bergeron isn’t all that much bigger of a character.
To understand the reference, look for an organization that is comprised of people who hold positions in all levels of society (education, real estate, law, banking/finance, medicine, government) who both have the capacity to make life difficult for people, and, whose members have built rockets and camped on the moon.
Milo Minderbinder (from Heller’s Catch-22) refers to a member of the same, or linked, organization.
So said an elementary school teacher of mine, anyway.