One of the themes you might like to consider is the fluidity of identity. On the face of it, it would appear that Eliza Dolittle's identity is fixed. She's a humble Cockney flower seller who looks set to remain in this lowly condition for the rest of her days. And yet Eliza, as a result of Higgins's experiment, is able to morph into a lady of quality and is able to take her place among the upper echelons of society without arousing the least soupçon of suspicion.
This stunning transformation would appear to suggest that identity is anything but fixed. On the contrary, Eliza's experience shows how it's possible for someone to put on a new identity and leave behind one's former self in the past. It's by no means an easy task, to be sure, and there are lots of bumps in the road along the way. But the very fact that someone from Eliza's humble background can become, to the outside world, a lady of refinement, bears eloquent testimony to the fluidity of identity in a society where appearance is everything.
I have linked below to the many themes of Pygmalion discussed on eNotes, including beauty, identity, appearance versus reality, and sexism. I will, however, talk about class, since that seems to me the most important theme of this play. Shaw was a Fabian, a kind of socialist who thought socialism could be brought about through reform, not by revolution. In the play, he attacks the British class system, in which the opportunities people had were based primarily on who their parents were—in other words, on the accident of birth. A class ideology or belief system insisted that people of higher class parents were genetically or innately superior to those of the lower classes, who were often thought to be born inferior or with a genetic predisposition to crime or immorality. In Pygmalion, Shaw explodes this myth of class by showing that Eliza, an impoverished flower seller, could, with a little training in how to speak and act like a lady, outshine the born aristocrats and become fit to marry a Duke (though she doesn't). Shaw also shows, in the depiction of Eliza's father, Mr. Doolittle, who comes into money, that it is economics, not birth, that determines who behaves morally according to middle-class norms.