Naruto-Uzumaki precisely is the symbol of whirlpool just as the headband. Naruto, the fishcake, came from its white on red pattern that resembles naruto-uzumaki.
The origin of the word Naruto seems to be "naru seto", the roaring strait, which is also the name of place famous for frequent whirlpools near Osaka. The word Uzumaki made of "uzu"(swirl) and maki(roll).
It happened to be the one of ancient symbols from the Stone Age as well.It has been used frequently on pottery, clothing and drawings, and the historians think it was to ward off the evil spirits.
As for Anime, I think both food and uzumaki(whirlpool) are implied, but only the author knows of which he was inspired first.