Sophie's recovery took longer after she gave birth to her daughter. It was really different from when she gave birth to her wolf pups. This experience gave her a different perspective on how much harder it was for a female human to give birth and care for their little ones.
She had not named her daughter because Sophie couldn't think of a good name in her current state. She wanted to name the youngest one something related to her family, but she already named her children from Leland with her parents' names.
Now, Leland didn't have a good relationship with both his father and mother and so giving a name based on his parents' names was not an option for Sophie. Also, even though the baby looked a lot like Sophie, she didn't want to call her Sophie Jr, or Little Sophie.
She immediately shot down Nicholas' suggestion when he brought it up.