I laughed out loud when I finally realized what band was saying this.

Humorously, the lead singer is named Jim (Adkins), but the band’s name comes from the backing vocalist/guitarist Tom’s brother, also named Jim.

The band's name came from a crayon drawing made after an incident between [Tom] Linton's younger brothers, Jim and Ed Linton, who fought frequently. Jim usually won, but Ed sought revenge by drawing a picture of Jim shoving the Earth into his mouth; Ed captioned the picture "Jimmy eat world".