In Fuller House, Duane makes an appearance in the episode "DJ and Kimmy's High School Reunion", where he uses his skills as a motivational speaker to help Kimmy overcome all of her embarrassments from that evening.
Kimmy: Duane here is a Shakespeare freak! Aren't you, my little Hamlet-and-Cheese?
Duane: (Chuckles) Whatever.
D.J.: Duane, you're into Shakespeare?
Duane: Shall I compare thee to a Summer's day? Thou art more lovely and more temperate. Rough winds do shake the darling buds of May, and Summer's lease hath all too short a date.
D.J: Wow, Duane, I had no idea you had such a sensitive soul.
Duane: (Voice cracks) Whatever.
Duane's last name was never revealed on Full House. However, in the Fuller House episode "DJ and Kimmy's High School Reunion", he's wearing a name tag giving his full name as "Duane Moffat".