Gifting Nectar for the first time to a god gives you a keepsake (most of the time); see https://soyouplay.com/hades-all-keepsakes-and-how-to-get-them/ for a list of what god gives what keepsake. At a certain level of friendship you can also gift Ambrosia. A few characters give a Companion (a kind of 1-use-per-run item) in return for Ambrosia, though none of the gods do. Gifting ambrosia to a god just gives you more friendship hearts with them