I agree with you, but I don't think you should consider the act of using multiple identities itself to be lying. Or at least, calling it that seems harsh. Do actors lie when they use stage names? Are authors lying when they publish under pen names?
Sure, some may use nicknames or professional names because they're more marketable. But others use pseudonyms for privacy protection. They want to compartmentalize their own identity, and I consider that a perfectly valid purpose.
Sure it's valid.. and in the US, if I'm not mistaken, it's expressly legal to call yourself whatever you want - as long as you aren't doing so to commit a crime.
So during day to day business and life, you can call yourself whatever you want. Others can insist on identification if it's important to them, and that gets trickier.. but using a pen-name on a book or a hotel reservation is no different than using a fake name at starbucks while waiting for your coffee.
Forging documents is of course illegal, so that puts a crimp on things - but there is no particular reason that you are required to use your "real" name except when dealing with government documents (and things that rely on them)
Those are both examples where you would heavily expect suspension of disbelief so I don't think they're analogous to the purpose the OP is asking about. You're not testing your skills against people, you're testing them for people.
Sure, some may use nicknames or professional names because they're more marketable. But others use pseudonyms for privacy protection. They want to compartmentalize their own identity, and I consider that a perfectly valid purpose.