You unlock a keepsake for giving a nectar to someone for the first time. You can check who can give you a keepsake in your codex. Those character who are eligible will have an empty heart container with a bow inside of it. This includes most the chthonic gods, all of the olympian gods, the shades on various floors, and
The last two will probably be the last ones you receive, as
isn't unlockable until you succeed for the 10th time, and
as well. Second spoiler keepsake is also the only one in the game that requires giving the person 2 nectars.