It's a private, voluntary, non-essential service. They can do what they want, short of protected class discrimination.
In other words, your name is what you agree to go by.
Also, you are not contractually bound by anyone to go by your given name, as you were not old enough to contractually agree to it when your name was given.
So in that situation, if you give an alias and you click agree to their contract, you would still not be in breach of contract.
They can always remove your account anyway of course.