Definition of "Eliza"

"My real name's !Eliza!. I've sometimes thought she called me after Eliza Doolittle in Pygmalion." "Come again?" said Sean. "Because she intended to do the same thing with me as Pygmalion did with Galatea and as Professor Higgins did with Eliza Doolittle, he remade her to be the way he wanted her, or let's say he had an ideal and he tried to turn her into that." - - - "She said she didn't, anyway, when I asked her. She just liked the name."

1993, Ruth Rendell, The Crocodile Bird, page 76