Squall had Raine's maiden name... or one that was given to him after he left the orphanage. Julia and General Caraway are Rinoa's parents, Julia died when Rinoa was five. Laguna and Raine are Squall's parents. Laguna went to Esthar to rescue Ellone, but then stayed there. He missed seeing Raine's new-born son (specifically mentioned in the game), and Raine died shortly after the birth anyway. Squall was sent into the orphanage. It's stated clearly that Laguna and Raine had a child together... but Laguna never met that child because he was in Esthar. The people of Winhiill hated Laguna, so they would've sent Squall to the orphanage under a different name.

Also, look at the evidence from Besimudo and IamTidus... that basically selas the deal.
Anyway, I think it's been officially confirmed that Squall is the son of Laguna, so there's not a lot to argue.