cock (n.1) "male of the domestic fowl," from Old English cocc "male bird," Old French coc (12c., Modern French coq), Old Norse kokkr, all of echoic origin. Compare Albanian kokosh "cock," Greek kikkos, Sanskrit kukkuta, Malay kukuk.

cock (n.3)

"penis," 1610s, but certainly older and suggested in word-play from at least 15c.; also compare pillicock "penis," attested from early 14c.

They're called peacocks because they're peafowl who are cocks. It's a way older term than the slang usage.