Alice's Adventures in Wonderland and Through the Looking-Glass
How we cite our quotes:
"Who are you?" said the Caterpillar.
This was not an encouraging opening for a conversation. Alice replied, rather shyly, "I – I hardly know, Sir, just at present – at least I know who I was when I got up this morning, but I think I must have been changed several times since then." (Wonderland 5.2-3)
Alice doesn't know who she is because she doesn't know where she is – and because she can't remember what she's been taught, in school or beyond.
She had had quite a long argument with her sister only the day before – all because Alice had begun with "Let's pretend we're kings and queens;" and her sister, who liked being very exact, had argued that they couldn't, because there were only two of them, and Alice had been reduced at last to say "Well, you can be one of them, then, and I'll be all the rest." (Looking-Glass 1.9)
Alice's slightly older sister seems to have moved beyond the ability to imagine (or perceive) the crowd of personalities inside her. Alice, however, can still play more than one role with ease.
The Gnat amused itself meanwhile by humming round and round her head: at last it settled again and remarked "I suppose you don't want to lose your name?"
"No, indeed," Alice said, a little anxiously.
"And yet I don't know," the Gnat went on in a careless tone: "only think how convenient it would be if you could manage to go home without it! For instance, if the governess wanted to call you to your lessons, she would call out "Come here – ," and there she would have to leave off, because there wouldn't be any name for her to call, and of course you wouldn't have to go, you know." (Looking-Glass 3.54-56)
The Gnat imagines that, without a name, Alice also won't have a social role.