Is it legal to have an alias name other than your birth name?

There is nothing to prevent you from holding yourself out to the public under an assumed name like a movie star, but you can only have one legal name, and in using an assumed name there must be no intent to defraud anyone or hide your identity from lawful creditors or law enforcement authorities, for example, and if a police officer asks you to identify yourself, you'd better use your legal name, not "Cher" or whatever.  When you ask how to go about getting an alias name legally, it's unclear whether you understand that even movie stars only have one legal name, which they use to sign contracts, etc. Their concern is to prevent other people from interfering with the development of their brand, which is associated with their name. That enters into the world of intellectual property law and trademark protection. That's only going to be an issue for you if you become famous.