I love this question, because I get it all the time when I talk to people in real life...like when the first thing my Aunt says after not seeing me for about 7 months is, "Where in the hell did you come up with the name Cherry Quench?"
So...my good Internet friend of 7 years or so and I were on Black Ops 2 one night. We don't very much enjoy playing Call of Duty multiplayer much rather than to chat. The newest trend of his (while not original) was to get high (kids, don't do illegal stuff) and play Black Ops 2 and just talk to me, while I'm a person that never takes any form of drugs, coffee, alcohol, etc. (I'm not fun to be around at a party).
Now I should preface what he said after achieving his...conscious status by saying that all of our weapon class names on any Call of Duty have odd-end names. It's usually combining two or more words in a weird fashion. Like...my classes would be named Badger Twist, Magenta Fart, Railroad Addiction, etc.
With that being said, knowing that I had my old name Reckoning Nite for about 5-6 years, my friend just says out of the blue, "You know what would make a good new Gamertag? Cherry Quench!"
"Yeah...," I said, as I put more thought into the associations of the words. "It's like a really cold, refreshing Hawaiian Punch or something."
And so becomes the genesis of the name.