Samus Aran's parents have never appeared in any of the video games, though they have in the comic books that can arguably be considered cannon. Her father's name was Rodney Aran, while her mother's was Virginia Aran.
She was attacked, along with her parents, by Ridley and the space pirates. During this time, Rodney shot the Afloraltite, which caused an explosion that killed everything in the territory other than Samus and Ridley, meaning he and his wife ultimately died.
Not much is known about her parents, though minor information can be taken from the comic book.