What is the name of the Cars Toons series centered on Mater's stories?

The Cars Toons series centered on Mater's stories is called Mater's Tall Tales.

Mater's Tall Tales is a series of short animated films produced by Pixar and Disney. Each short presents Mater claiming that he played a remarkable role in an event, then expands the claim into an exaggerated adventure involving characters from the Cars world.

The first short, “Mater the Greater,” premiered in 2008. The shorts use a framing joke: after Mater tells his story, the other characters often discover that parts of it may have happened, even if his version is wildly embellished.

The series is separate from Pixar's Cars feature films, although it uses their characters and setting. It was followed by Cars Toons: Tales from Radiator Springs, another collection of shorts released in 2013.