Creating a fictitious persona is not unlawful. You may, for example, construct a website with a completely new character. However, if you use that fictitious identity to perpetrate fraud, such as submitting an insurance claim or acquiring prescription medication, that's a different problem. It's called "fraud" because it has the potential to deceive others; therefore, it is a crime.
It's also worth mentioning that creating multiple identities for yourself is considered fraudulent behavior as well. If you have one Facebook account in the name of "John Doe" and another in the name of "Jane Roe," then you are being deceptive about your identity. As long as you have the permission of each individual involved, it isn't illegal but it can lead to problems with fraud prevention programs used by social media sites.
Finally, it's important to note that creating false identities to avoid prosecution or punishment for other actions is not only illegal, but also protects you from going to jail for those other actions as well.
So, when it comes to constructing a false identity, there are degrees that are permissible and particular behaviors that are prohibited. Identity theft and identity fraud are both criminal under federal law in the United States. In general, however, providing a fictitious identity is not criminal as long as it is not done as part of a deception. For example, if I write "John Doe" on an employment application because that's the only name known to me, I'm not committing identity theft because I'm not using someone else's identification number or credit card. Similarly, if I use the "Doe" name to get medical treatment at a hospital that does not ask for any form of ID, there is no crime involved.
Now, if I use the "Doe" name to get a job at a company that requires a valid ID card or driver's license, that would be identity theft because I would be using someone else's identification information without their permission. The same thing applies if I use the "Doe" name to rent a house or move into an apartment. There may be some situations where you cannot prove who you are without showing some form of ID, such as when checking into a hotel or holding a bank account. In those cases, creating a false identity would be a problem.
Finally, if I use the "Doe" name as an online password, that would also be identity theft because I would be utilizing someone else's identifying information without their consent.
False identity fraud happens when a person develops a false identity in order to engage in criminal activity. Once they have this knowledge, they make up their own characters rather than imitating an actual person. They may, for example, combine a current social security number with a fictitious location and identity. These people then use this fabricated identity to file fraudulent tax returns, steal money from bank accounts, or commit other crimes.
The term "false identity" is also used in reference to cases where someone uses the name of another person without that person's consent. This may be done to conceal their own identity or because they receive some kind of financial benefit (such as avoiding prosecution for a crime they have committed). For example, two criminals break into a house; during the burglary, one of them hits the victim over the head with a club and both flee the scene. The next day, the police search for witnesses who can identify the perpetrators. One witness claims to know something about the crime but won't talk unless she is given a police officer's name to call. The other witness says that he saw two men running from the scene but can't give any more information until he is given a number to call. He is then asked if either of these numbers is his wife's or daughter's. He replies that they are not but that he will call back in five days if it helps solve the case. After five days have passed, the witness calls back only to find that neither number belongs to anyone's family member.