Character Analysis
U's number is never given. D-503 wants to preserve her anonymity:
I prefer not to give her Number, for I fear I may not write kindly about her. (10.2)
She's the controller in his apartment who brings him his pink cards and other official notices. She's also an educator of small children. Her role here is ultimately antagonistic—she serves the state and is willing to turn in D-503 if she takes a mind to it—but she also shows some signs of affection towards him and he returns it. In that sense, she closely resembles the State itself, and D-503's often conflicted relationship with it. The book often describes her as fish-like, or having "the gills of a fish," (10.2), which is supposedly the quality D-503 dislikes most about her. Ironically, it's the one he uses to describe her most often (go ahead, check the book for fish gills references). Again with the "conflicted feelings about the state" thing.