A funny name, but it comes from an even funnier story from DCist.
A few years ago, a customer named Jeff Simmermon went to Murky Coffee and ordered the same thing, espresso over ice. The employees refused to serve him, saying it was against their coffee policy, and responded rudely, rolling their eyes. Instead he asked for a triple espresso and a cup of ice, and received it with more eye rolls. He then got in a debate with the barista, who said they didn't like people doing that because it affects the taste of the espresso and he said he could drink it however he wanted, basically.
Simmermom got angry, later ordered another drink, then wrote "fuck you and your precious coffee policy" on a dollar bill and tipped the barista with it. He then wrote a blog post about the experience, which got picked up on various other sites.
Then Murky's owner, Nick Cho, responded on his own since-deleted blog angrily, mentioning the coffee policy and threatening "if you ever show your face at my shop, I'll punch you in your dick." Cho mentioned something about Simmermon threatening to burn his store down, but I can't find that. (Another reason Cho was opposed to the practice was that people could theoretically get espresso shots and add lots of milk, making their own form of a latte but avoiding paying full price.)
The argument caused even more hubbub, with most people siding with Simmermon, who admitted on his blog that he acted like a dick too. The Washington Post wrote about it and the whole story took wings, with Junkpunch becoming a common joke on DCist and elsewhere -- Big Bear amusingly promised not to punch you if you ordered it. Simmermon later did a spoken word/story thing about it.
Espresso over ice is still kind of a big debate too. (And Cho was later charged with tax fraud after not paying sales tax or corporate tax for years, so there's that.)
And now you can get a Junkpunch in our area! Kudos, Qualia.