Quote 13
"No, I've made up my mind about it: if I'm Mabel, I'll stay down here! It'll be no use their putting their heads down and saying 'Come up again, dear!' I shall only look up and say, 'Who am I, then? Tell me that first, and then, if I like being that person, I'll come up: if not, I'll stay down here till I'm somebody else.'" (Wonderland 2.9)
Wonderland is a place of fluctuation and change. Alice determines to let her identity keep shifting until she's happy with it, and only then to return to the "real world" where identity is static.
Quote 14
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.
Quote 15
"This must be the wood," she said thoughtfully to herself, "where things have no names. I wonder what'll become of my name when I go in? I shouldn't like to lose it at all – because they'd have to give me another, and it would be almost certain to be an ugly one. But the fun would be, trying to find the creature that had got my old name! That's just like the advertisements, you know, when people lose dogs – 'answers to the name of "Dash": had on a brass collar' – just fancy calling everything you met 'Alice,' till one of them answered! Only they wouldn't answer at all, if they were wise." (Looking-Glass 3.64)
Alice imagines that her name and her person are separate but stable things; if they became separated, the name and the identity that went with it would still exist somewhere in the world.