Its probably not illegal unless the alias is adopted to misrepresent something to someone, or in attempt to avoid a legitimate liability. You can always change your name formally via court filing.

Are you allowed to use a fake name?

People use fake names on the Internet all the time—but that doesnt make it legal. Whether for Facebook accounts, Xbox Live, or a pointless survey that your friend asked you to fill out, using a fake name online in any capacity could get you arrested.

Can a lawyer use a fake name?

In the first, a lawyer wants to use a pseudonym to write murder mysteries. For nonlegal activities, a lawyer may “adopt any name by which the lawyer chooses to be known.” For their law practice, however, lawyers should not use a name that is materially different from the one on bar records, the opinion says.