What is the name of the judge in the town of Radiator Springs in Cars?

The judge in the town of Radiator Springs in Cars is Doc Hudson.

Doc Hudson serves several roles in Radiator Springs: he is the town's medical doctor, its judge, and later Lightning McQueen's mentor and crew chief. Although the film presents him as a quiet local physician, his past is far more impressive than his modest role initially suggests.

Doc is a 1951 Hudson Hornet who once competed as the famous Fabulous Hudson Hornet. After a serious racing accident ended his career, he withdrew from the racing world and settled in Radiator Springs. Lightning's arrival gradually draws Doc back into competition and forces him to confront his old identity.

The answer can be confused with Sally, Mater, or Luigi because each has an important civic or professional role in town. Sally is the local attorney and motel owner, Mater is the tow truck, and Luigi runs the tire shop. Doc is the character explicitly identified as Radiator Springs' judge, while also acting as its doctor and Lightning's mentor.