Why has Shaw chosen to use an allusion to Ovid's myth as his title for Pygmalion? How does it contribute to emerging themes in the play?

In Ovid's myth, Pygmalion is the name of a man who carves an ivory statue and falls in love with it. He is so in love with it that he wishes it would come to life, so he could marry it. Aphrodite, the goddess of love, grants Pygmalion's wish and turns the statue into a woman. 

In Shaw's play, Henry Higgins acts like Pygmalion. He creates or "sculpts" Eliza Doolittle into a completely new person...

In Ovid's myth, Pygmalion is the name of a man who carves an ivory statue and falls in love with it. He is so in love with it that he wishes it would come to life, so he could marry it. Aphrodite, the goddess of love, grants Pygmalion's wish and turns the statue into a woman. 

In Shaw's play, Henry Higgins acts like Pygmalion. He creates or "sculpts" Eliza Doolittle into a completely new person by retraining her accent and speech and teaching her to behave like a lady. The title isn't entirely flattering, for Higgins sees Eliza as an object, a "thing" he has created for his own convenience, and not a person. 

After he successfully turns her into a lady who can hold her own in the highest society, she does come to "life": she stands up to him and fights back against his verbal abuse. At this point, he starts to appreciate her. He doesn't want to marry her, but wants her to stay with him as a "bachelor." She is, to him, still his creation, and he is surprised when she leaves. The idea of Eliza being seen as a "statue" or "object" underlines the feminist themes of the play: Higgins might think Eliza belongs to him, as if she were a sculpture, but, in fact, she is her own person.