This, pretty much. I have a friend who had to change her (legal) name due to a stalker, and consequently never uses it anywhere online (she uses an alias on facebook).
Given that's a lie about her identity, she could be quickly distrusted if she ever appears in a court. And that's a preety huge consequence of the Real Name Policy.
"Changing a legal name" is a legal process and the result, a new name for the same person, is no more a lie than choosing a nickname for oneself. From a legal standpoint, the changed name is now a legally permissible "lie."
This does not result in mistrust by a court because the legal system was involved in the change. Of course, all this assumes the "change in legal name" went through the legal process.
Actually changing your "legal name" in many places isn't a "legal process" at all. Not if you mean a state-managed, form-filling exercise.
In the UK for example the law only specifies you must make a public declaration of your intent to use a new name (a notice in a local newspaper will do), and then completely abandon any all use of the old name. Even the venerable old 'Deed Poll' service is just a mechanism to make that initial declaration, it's actually a private register.
In the U.S. anyway, you have the right to use any name by which you represent yourself consistently without intent to defraud, much akin to a common-law marriage.
The changed name is NOT a "lie". Changed name is her new name. As far as law is concerned, new name is the truth about her identity.
And I'm not sure that court would take it against person if that person uses alias online. After all, it is general advice for teenagers not to reveal their names online.