I give out awards on a daily basis. However, I never knew the actual terminology for the person who hands out awards. I was thinking of awarder but that doesn't seem right.
According to Merriam-Webster, it is a presenter:
one who presents something : a person who formally gives or bestows something (such as an award) or who brings something before the public
// The presenter of the award for Best Actress was the actress who won the award last year.
This site uses an awards presenter. If the people to whom you are describing your job are likely to be British English speakers, it is better to use this longer phrase, as in British English, a presenter is
a television or radio broadcaster who delivers news or information to an audience (Merriam-Webster)
A related concept is that of an MC (master of ceremonies). Again from Merriam-Webster:
:a person who acts as host at a formal event
:a person who acts as host for a program of entertainment (as on television)