Following the Nebuchadnezzar's near-destruction, Morpheus recruited new crew members from the ship, the Enki, among them Apollo.  Apollo was the rough equivalent to replace Dozer, who was killed by the treacherous Cypher.  Apollo, while also having hacking skills and relative fighting skills within the Matrix, is first and foremost the doctor of the Neb.

Apollo (or 'Pol' as the crew calls him) is a very pale individual -- not the least because he has pale blond hair.  His nom-de-hack is due to the fact that he is twins with his sister, who goes by Artemis.  It might also be because Apollo (the Greco-Roman god) was responsible for the Hippocratic Oath and other medical-related stuff.

Apollo, while not being as aggressive as his sister (and even being turned off by her nature), was very attached to his sister.  When she was killed by Agent Jameson, he was very distraught and even questioned his medical skills, but recovered enough to cope.  This didn't stop him, however, from being cold to the hacker Heph, who was transferred from the ship Jericho to replace Artemis.  Apollo didn't take kindly to the thought that someone could replace his sister.