From the China Lake website:

"China Lake's 5-inch Zuni rocket was heavily used over the years. China Lake
was the lead laboratory for the 2.75 and Zuni developments. The Zuni, as
well as some other early unguided rockets, was originally conceived as an
air-to-air weapon, but the rocket's role evolved into that of an
air-to-ground weapon. Interestingly, the Zuni shot down a MiG-15 early in
the Vietnam War when the MiG let itself get ahead of an A1 Skyraider that
was trying to evade it. The Skyraider fired a Zuni and scored a hit. (circa
1956) "

So in response to the original poster's question...I don't know why they
called it Zuni, but someone who worked at China Lake in the 1950s would
probably know the answer. Or perhaps a current day China Laker who is
familiar with the history.

JD