I recently saw someone refer to Michele Bachmann as Michele Botchman [emphasis added] and was wondering what the term for such a parody name would be? Obviously it was intended as pejorative, so I'm not sure if "parody name" is specific enough.
The term dysphemism seems appropriate:
A derogatory or unpleasant term used instead of a pleasant or neutral one. The opposite of euphemism.
ODO, emphasis mine
Politicians brand themselves to generate pleasant feelings among voters, but these monikers are floated to defame them with a sense of contempt, as the specific meanings of the prefix and root imply:
I can also recommend the portmanteau neologism slurbriquet.
3 chiefly US Make damaging or insulting insinuations or allegations about:
ODO, emphasis mine
A person’s nickname:
Michelle Bachmann's opponents have adopted a convenient slurbriquet: Botchmann to emphasize her bungling attempts to articulate unpopular positions.
No special name that I know of, no. However, this is the sort of concept that would normally be expressed by a noun compound, and Pejorative Parody Name is a good descriptive choice. If you're thinking about using it, though, you'll still have to give examples to people who've never heard or thought of it before.
Pejorative Parody Name also has the benefit, with increasing familiarity and use, of being recursively shortenable all the way to the TLA PPN (being a TLA is the true mark of acceptance by Norma Loquendi, who also likes OCS a lot), with interesting stop along the abbreviation route for creation of terms like PP Name (which has an interesting sound to it). Etc.
It might well catch on. On the other hand, so might Michelle Bachmann. It's happened before.
The phrase that I see commonly is "deliberate misnaming".¹ It seems to cover intentional slurs by misspelling, such as "M$" for "Microsoft" or "Democrat Party" for "Democratic Party".
This is a type of malapropism:
malapropism, noun : an act or habit of misusing words ridiculously, especially by the confusion of words that are similar in sound.
It Bachmann's case, it stemmed from an incident where she mispronounced chutzpah as choot-spah, leading some to observe:
If Michele Bachmann gets to pronounce chutzpah "choot-spa," then we now get to pronounce Bachmann "Botch-mann."
Derogatory nickname (two words) or epithet might work, but they are not necessarily variations of the original name being made fun of, and epithets are not necessarily abusive.
Name squib might be an appropriate term. Among definitions of squib are "petty lampoon", "political joke, printed and circulated at election times against a candidate, with intent of bringing him into ridicule, and influencing votes", and "small satirical or political temporary jeu d'esprit, which, like the firework of that denomination, sparkles, bounces, stinks, and vanishes".
Also note that while caricature typically means "A pictorial representation of someone in which distinguishing features are exaggerated for comic effect" it also has the meaning "A grotesque misrepresentation", so one could refer to name caricatures.