I’ve often seen this stated as the law in the U.S., but I find it a bit questionable. I don’t know of any law that prohibits you from using whatever name you like, and I appreciate the logic of saying, “if it’s not prohibited, then by default it’s legal.” But I’m not sure it really plays out that way.
In particular, there are many contexts in which you are prohibited by law from providing any false or misleading information to another party. This would be the case in applying for a bank loan, for instance, or reporting your income taxes. There are many other situations covered by such laws – so many that it would be difficult to list them all (even assuming I knew them all, which I surely don’t).
So here’s the big question: if someone asks you to provide your name, is it false or misleading to give them a made-up name that you’ve never used before? I think that many people would say, “yes.” I’m sure you can come up with arguments to the contrary, to the effect that your name is whatever you want to call yourself (don’t get all hung up on labels, man) but I’m not confident that these arguments will be well-received by law-enforcement authorities or a jury. If you were to get caught trying to borrow money from a bank using an “alternate” name, and the bank reported you for bank fraud, I’d advise you to hire the best criminal-defense lawyer you can afford, pronto.
Even outside of situations that aren’t covered by a law of that sort, I’d worry about the “as long as it’s not fraudulent” rule. Keep in mind that, if you get into a dispute, your conduct is going to be judged by some third party (cops, prosecutors, jurors). In the eyes of many people, using a “fake” name just looks fraudulent, on its face.
I’m not trying to say that you can’t ever use a name other than your “real” name. There are some situations in which using different or “fake” names is socially sanctioned and expected, such as actors using stage names, or married women using one name professionally and a different name in their personal life. Also, it’s probably ok to use whatever name you want in purely social situations, like parties.
But in my personal opinion, if you’re dealing with the government, or you’re dealing with private parties in a situation where money is changing hands, using a “fake” name (without disclosing that it’s not your “real” name) is asking for trouble.
Of course, this whole issue is becoming academic, since it’s hard to do much of anything these days without providing ID or a social security number.
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Standard disclaimer: Nothing in this post is legal advice, and I’m not your lawyer. Consult an attorney if you have a real-life question.*