In another world, Sirius would have been named Teddy's godfather. Or so Remus sometimes thinks. In truth, he knows that if Sirius was still alive then Teddy would likely have never been born. It would still be the two of them, and Dora would never have happened. Unless Sirius had tried to talk him into the possibility, which frankly he could see happening. ("You've always wanted a family, Remus. She can give you that." And even if Sirius had tried to persuade him about Dora, he very much doubts if he would have gone for the idea. Sirius was always enough for one man to deal with.)
Teddy belongs to his new life now (not that new, perhaps, with battles to be fought and full moons to deal with still) so perhaps it's right that Sirius cannot be a part of it (he was never the same after Azkaban). But, God, how he wishes sometimes that Sirius could be a part of this. Could meet his son and tell him stories of their youthful adventures, could be a part of the family. It's one of the things that hurts the most in this new reality - the knowledge that no matter what happens to him Sirius will never know. That hadn't mattered during the Azkaban years, as so little else seemed to matter too. But now . . .
(And maybe they should have had some reference to Sirius in the child's name. In some ways, he is a Black too. He should know how brilliant his cousin was, how much he really mattered.)
It's only right that Harry be godfather. He is the only one left with some connection to the way things were. (There is so much of James and Lily in him - he sees it more every time that they meet. But there is Sirius there too - Sirius' nerves and concern the first time he held Harry reflected in Harry holding Teddy. How the circle has come around.) And should something happen to him and Dora, Harry will understand how it feels to be an orphan, will do his utmost best for Teddy. That's what matters now.
(No matter how many times he tells himself that, he still has a hard time believing it.)