From A Wiki of Ice and Fire
|Book(s)|| A Game of Thrones|
A Storm of Swords
While Eddard is out on a ride with Robert, the King asks for the name of that one woman of his, the bastard's mother, and Eddard replies that it's Wylla. Eddard then states he does not want to talk about it. Robert then adds that she must have been quite a woman, if she was able to make Eddard Stark forget his honor even for an hour.
Lord Edric Dayne tells Arya Stark that he and Jon Snow are "milk brothers". He elaborates that one of the servants of his house, called Wylla, was Jon Snow's mother. When his own mother had no milk, Wylla became Edric's wet-nurse. Since Edric is about four years yonger than Jon, this must have been long after Lord Eddard brought Jon to Winterfell. According to Edric, Wylla worked for many years at Starfall. Arya, who has never heard the name and is aware that Jon doesn't know anything about his mother, first thinks that Edric might be mocking her, but when he swears on the honor of his house that he's telling the truth, she decides to remember the name, so that she can tell Jon when they meet again.