“Navy” is an up and coming name for girls in the US, according to the Social Security Administration.
Um. Well. I don’t want to be too negative, because it’s certainly patriotic. But you do realize that there are certain traditional connotations about young women vs. young military men, right? If you are naming a girl after the color, maybe you should pick another shade of blue? (Indigo, Azure, stuff like that. But those probably make better middle names.)
There’s an Indian name, Anavi (“kind to people”), that has the nickname form “Navi.” Other names from India include Navya, Navita, and Navistha. Some of them refer to the Sanskrit for “new.”
There’s a Hebrew girls’ name, Navi, which apparently means something like “named.” I don’t know if it’s an allusion to the Name of God, but normally that would be Shem.
The Hebrew word for “prophet, seer, one who sees” is pronounced “Na-BEE” and usually spelled “nabi.” (So if that is the name you want for your kid, please spell it that way.)
The feminine form (“prophetess”) is “nebiah” (nuh-BE-ah) or “hannebiah” (HA-nuh-BE-ah).
That said, there is a traditional connection between the Church and St. Peter’s fishing boat, and hence with the Church as a ship or as Noah’s Ark. So yes, there was a St. Navida (martyred in Africa) and a St. Navigia (at St. Etienne d’Auxerre).
Nautica would be an okay name, although everybody who speaks English would call the girl “Naughty.” Also, it’s a clothing brand.
Nausicaa is a pretty name, if you want to go all classical. She was the (probably a fairy) princess who found Odysseus shipwrecked on the shore, and kindly helped him out. (Although what her name means is “burner of ships.”)
Other pretty names come from devotion to Our Lady of the Snows (Aug. 5), like “Nieves” (Spanish). There’s also the related names “Nova,” (Latin for “new”), “Novita,” and “Novella” (although that’s a literary form now, so probably not a good plan).