Disclaimer: Naruto isn't mine
Being a dad means realizing that more than a baby has been born. So has a father.
A lot of people assumed that when Sasuke got around to rebuilding his clan that he would just leave the children in the care of whatever luc-poor girl that Sasuke got married to. Sasuke would still be around of course, but he wouldn't go out of his way to spend time with his children unless it was to help them train. Sasuke wouldn't do that. He also needed to check if his children had the Sharigan.
Truth be told, Sasuke didn't want that rumor to be true. He wanted an active role in his children' life. He wanted to be a father not a father figure. He had no idea how that silly idea happened to come about.
That little fact never truly hit him until Naruto went into labor. Sasuke sat outside in the waiting room staring at the walls, the clocks, the newspaper, the front desk, everything, with a voice in the back of his mind telling him that his last life goal was being accomplished.
One the doctor said the c-section was complete and Sasuke could go see Naruto and the baby, Sasuke had to mentally prepare himself. He wasn't Sasuke Uchiha- Konoha resident, nor Sasuke Uchiha – Uchiha Clan Avenger, he wasn't even Sasuke Uchiha- husband to Naruto Uzumaki-Uchiha.
He was Sasuke Uchiha – father.