This is true, however, in the case of the "Zulu" Cobra this is a phonetic designation rather than a name relating to Native American tribes - especially since the name of the helicopter is cobra and not a Native Name like Sioux or Lakota.
Take the "Whiskey" cobra as an example, there is no Native American tribe called Whiskey, but Whiskey is part of the Phonetic Alphabet, which the US uses to demarcate different blocks. the AH-1Z being the most recent, and probably the last of the AH-1 line for the US military, hence it's "Zulu" designation.
It's the same phenomenon seen in this article with the mention of the F-15 "charlie"
F-15 fighters have been flown since the 1970s, with the single-seat “Charlie” version that crashed Wednesday first appearing in the latter half of the decade, Air Force officials say.
After crash in Virginia, a brief history of F-15 fighter jet mishaps - The Washington Post
See the above explanation to answer your question.