Mars is named after the Roman God of war; both the god and planet are associated with war and death.
Most of Mars' mission names are all named after geographical locations on Mars.
Ultor is an exception; it is instead named after one of Mars' epithets, Mars Ultor ("Mars the Avenger" in Latin).
Kadesh is also an exception, named after a battle between Egypt's Ramses II and the Hittite empire.
The fact that both the Corpus and the Grineer are present on Mars is a nod to The Gradivus Dilemma, which ended with the Grineer taking over several nodes originally controlled by the Corpus. This makes Mars the only planet where all three major enemy factions are present.
Mars used to be a purely Corpus-controlled planet from Update 14 to Update 15.13, where several nodes were given to the Grineer.