Mars itself was named after the Roman God of War which derives from Roman Mythology and according to the Roman Myth itself mars rode on a chariot pulled by two horses named Phobos and Deimos (meaning fear and panic) and the 2 small moons of mars are named after these 2 horses.
First of all before the Romans themselves named the Red planet Mars Greeks themselves were actually fascinated by the Red planet itself and due to the planet’s own blood red color led them to attribute the planet to Ares which is a god that is part of Greek Mythology and once/as the Romans themselves conquered the Greeks they renamed the gods and the planet Ares became the planet Mars.