They can do what they want within the law, and there is AFAIK a common law right to use aliases.
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.
Yes, but if they give you a contract that says that you have to provide them with your birth name to use their service, then that part of the contract just doesn't count either way in those territories where it has no legal basis.
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.
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.