how did Mimas become Mimas?

Mimas is named after a character in Greek Mythology:

Mimas 

Mimas was a Giant in Greek Mythology. His mother was Gaia and his father was Uranus. Just like his Giant siblings, he had serpents for legs and was born in full armor. Mimas was killed by the Greek Olympian Hephaestus during the Gigantomachy, or the war between the Olympians, led by Zeus, and the Order of Chaos, led by Alcyoneus. 

The family tree of the Greek gods, starting with the Titans.

The Greek god Hephaestus, who killed Mimas.