あお (ao) is a noun which means "the color blue". For example, if someone asks you what color you like, you can say "Ao ga suki desu" (I like blue).
On the other hand, あおい(aoi) is the adjective form of あお (ao). For example, you can say "aoi isu" (a blue chair) or "kono isu wa aoi desu" (This chair are blue).
As you mentioned, there are people named あおい. It can be their first name as well as their last name. Usually, it has nothing to do with the color blue unless it contains the kanji 青 (it is the kanji meaning the color blue) .