The story
The attribute “Maine” is after the region where the breed originally became popular. For the second part, there are several theories. The dominant one is that it refers to a resemblance of the breed to the raccoon, leading some to propose the theoretical impossibility of the cat being a crossbreed with the raccoon. Another theory is that the name derives from a legendary Captain Tom Coon, who is said to have brought over such exotic cats.
Etymology from Wiktionary, CC BY-SA 4.0.