|MadSci Network: Science History|
The name quark itself comes from Dr. Murray Gell-Mann showing off how cultured he is, demonstrating that he'd waded through James Joyce's impenetrable Finnegan's Wake enough to find this: "Three quarks for Muster Mark!" which in fact is part of a drinking song.
As for quark "flavor" (the term physicists use to talk about types of quarks), that was coined by Dr. Harald Fritzsch.
"It deserves its name from a discussion I had with M. Gell–Mann in 1970, when I was a graduate student, working with Gell–Mann at CALTECH. One day we stopped on the way back from lunch in the Baskin–Robins place in Pasadena. When we had icecream, I remarked that the 32 flavors, offered by Baskin and Robins, are much more than the three flavors u, d and s, we are dealing with in case of the quarks. Gell–Mann got hooked on this remark, referring to the physics of flavor in the future, when we were dealing with the weak interaction of the quarks, and not with the colors, reserved to the description of the strong interaction."
--From "The Physics of Flavor - Challenge for the Future", H. Fritzsch, J.Korean Phys.Soc. 45 (2004) S297-S300
Thanks to Dr. Brian Fields (a particle astrophysicist) for his help with this answer.
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