Eugene is a blue Whatnot who plays the tuba for the Muppet Orchestra in It's a Very Merry Muppet Christmas Movie.
When Miss Piggy falls off the stage and into the orchestra pit towards the end of the movie, she lands on Eugene. Although he survives the impact, his tuba isn't so lucky.
Eugene hopes that Kermit's love can fix his tuba, and Kermit assures him it will.
At the last moment, while shooting, Bill Barretta asked Steve Whitmire (performing Kermit) to address this musician character as Eugene. It was an inside joke for his brother, Gene Barretta.