Question: How come this movie barely showed anything about Luke and Leia's mother? Luke doesn't even ask anyone what her name was (maybe that was hidden from Leia, but he can probably guess that Yoda or Obi-wan would know). I know we can assume that she was discussed off-screen, but they could have revealed a little more about her.
Answer: Why can we assume that she was discussed off-screen? Luke's got more important things to talk about than who his mother was. Yoda dies shortly afterwards and Luke's understandably more interested in how Darth Vader, given that he's got to go up against him, can be his father when talking to Obi-wan's ghost shortly after. Not a lot of time for general chit-chat. Behind the scenes, at that point, very little would have been decided about their mother, as it would be irrelevant to the plot of the trilogy and to discuss her on-screen would have wasted time and slowed everything down.
Answer: The Jedi are shown to have something of a blind spot in regards to matters of the heart. Note that when Luke confronts Obi-Wan over lying to him about his father's fate, Obi-Wan's response is haughty and defensive, and gives Luke nothing in terms of regret or apology. They're focused on their mission, not on how Luke feels. Why waste time, in their eyes, telling Luke about his mother? If they had their way, he wouldn't even know about his father. The prequels would make this more explicit, showing that the Jedi are conditioned from the beginning to let go of all "passions" because they could so easily be corrupted, and their inability to understand Anakin's emotions just contributes to his downfall.
TonyPH