Reichu: Toji's little sister is one of the characters whom we hear about a few times but never actually see. (There are quite a few of these in the "cast".) I'm not sure if there is any specific reason why Anno keeps her off the screen. If NGE were "any other anime", one might have expected to see her once or twice.
OMF: Even though we never see her, her presence really never leaves.
HeWhoPostsStuff: Although the anime never names her, a bunch of fanfiction writers more or less came to a consensus on what to call Toji's sister in their stories, I forget what it was though… "Maiko", or something along those lines…