Suzy is Gingy's former girlfriend. She is a minor character voiced by Susan Fitzer.
Shrek the Third
Suzy makes a brief appearance in Gingy's series of flashbacks when he was confronted by Captain Hook during the interrogation scene. She and Gingy were shown kissing in a car at a drive-in theatre.
Shrek the Halls
In Gingy's Christmas story, he recounts a Christmas winter night spent with his girlfriend Suzy. The two were in a car parked on a table which made them seem like cookies left out for Santa Claus, who later tries to eat them. The gingerbread couple attempted to run but Suzy was caught by Santa and she was eaten after letting out a scream.
Her death has caused for Gingy to have an absolute fear of Santa, clearly shown at the end of Shrek the Halls when he screams and runs to hide inside Shrek's house upon the sight of Santa in the sky.
Gingy's friends did not know of Suzy's story prior to this, raising questions as to whether or not he had invented the story. However, this would conflict with his apparent fear of Santa.
Shrek Forever After
While she is not shown in the Shrek Forever After film, Suzy is mentioned in a skit (Gingy's 'Lil Sugar) in the original soundtrack album. Gingy calls into the Rumpelstiltskin Show to give a shout-out to his "sweet, sweet girlfriend Suzy".