Olimar's son is introduced in Pikmin in the log book, along with the rest of the family, including their dog Bulbie, and in Pikmin 2's space e-mails. It seems that he wants to visit the Planet of the Pikmin, and was upset that his father went back to the planet a second time without him. His e-mails imply that he really admires his father's being a Space Captain.
In the game files of Pikmin 2, the folders for the captains include "orima" (Captain Olimar), "orima3" (Louie), and "syatyou" (The President). "orima2" was removed, and was supposed to be Olimar's son.