While Orion is typically a boy’s name, there is no equivalent name for a girl (like Samuel for boys and Samantha for girls). That being said, there is nothing keeping people from naming their girls Orion.
Some people point to a star within the constellation of Orion named Bellatrix. The name Bellatrix means female warrior.
While it is not quite the same as an origin with the meaning mountain, nor is it similar sounding to Orion, Bellatrix is a companion to the name Orion because of its inclusion in the constellation.