Given that aliases are legal and not in and of themselves considered fraudulent in most of the world, the requirement to use a 'real name' for online services seems to have no real legal basis anyway.
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.
We'll all be skeptical when Google try and tell us anything else.