This came to me immediately after I saw the episode. It wasn't until after I wrote this that I found out that there are two stories that are similar enough to cause problems if someone suspects plagiarism, which I promise I did not intend. This story was written long before I was aware of any similar ones. If either serendipitysidle or MHfan11794, the authors of those fics have a problem with this, I'll remove it from the site.
Paternity: Alternate Ending
Elliot Stabler rushed through the hospital toward the room he'd been told his wife was in. Just ahead of him he saw his partner, Olivia Benson. She looked anxious. She started to speak, but he just moved past her into the room—and saw his wife and newborn son resting comfortably on the bed. After meeting his son and making sure both were well, he stepped back out into the hall where his partner was still waiting. She smiled at him, tired, but relieved.
"How's the baby?" She asked him. He smiled back.
"Great." They both started to turn and go, when Elliot suddenly pulled Olivia into a hug. She closed her eyes and returned the embrace. Neither of them spoke. There was just a sense of gratitude that was too great to be expressed with words. After a moment, the hug ended, and they continued on their way out. Olivia looked at Elliot.
"You pick a name?" He smiled again.
"Kathy wants to name him after you." She looked puzzled, and he clarified. "Benson." Olivia looked startled, then very touched. She considered it.
"Benson Stabler." She grinned. "Sounds like a good combination."
Again, if either of the aforementioned authors, or anyone else has a problem with this story, I'll take it down. Once I figure out how, that is. I don't want any trouble and I really don't want to get booted off the site. Please review!