He stayed with her. She'd been half afraid he wouldn't. Half afraid that he'd deliver her to hospital only to turn right around and walk out the doors again. But he didn't. He looked completely ill and more than one nurse had asked him if he needed to sit down, but he'd stayed.
And then there she was. Their daughter. Tiny and perfect with a shock of dark brown hair that looked so much like his (it even stuck out in a little peak in the front!) she wanted to laugh and cry at the same time. He'd almost refused to accept her when the nurse handed her over with a, "here you go, Dad!" He still looked like he might vomit, but he didn't. He just gazed into her tiny face, and Rose watched as he fell in love with their daughter.
He'd nearly panicked when the nurses had taken her back, explaining that they needed to run some tests. Rose had needed to intercede, explaining that all babies needed to have blood drawn and be weighed and measured before being released to their parents' care. It occurred to her that he had no idea what the protocol was for human births. He anxiously paced the room and babbled about nothing the whole time she was gone.
When the nurse came to ask them what name to write on the birth certificate, they'd both been struck speechless for a minute. They hadn't picked one yet, Rose explained. Tomorrow? The nurse smiled, agreed that naming a child was an important decision, and told them she'd be back when they'd made a decision.
"I was thinking Elizabeth," she'd told him softly after the nurse had closed their door.
"Elizabeth is good," he agreed, unable to take his eyes off the baby's sleeping face.
"Do you…I mean, I know naming is a serious thing on Gallifrey. Do you…want to give her a Gallifreyan name?" She held her breath. His own name was still a mystery to her.
"She's human," he said, simply. "Elizabeth is lovely. Very English."
So she was Elizabeth.