Mr. Doyle is a teacher at Cypress Creek Elementary School.
He started to teach his class before he realized Bart couldn't read cursive. He then asked Bart if he knew multiplication tables and long division, which Bart did not, arguably due to the lackadaisical teaching work of Mrs. Krabappel, combined with Bart's obstinacy towards learning new subjects. Mr. Doyle is last seen leading Bart into the "Leg Up" program, which he ordered Bart transferred to in an attempt to bring Bart up to speed with his fourth-grade class.
Behind the Laughter
His name was not revealed in the episode. It was revealed in Simpsons World: The Ultimate Episode Guide, Seasons 1-20.