While misrepresenting yourself or your credentials can be fraud, the title of PhD/Doctor (outside of MD) is not regulated, at least not in the US. It’s almost like an endorsement from the university that you passed their tests.

But that’s not very regulated either, and there are countless certifying boards (Boards of Regents, typically).

Falsely claiming to have a PhD in Neuroscience from Harvard, or an honorary Doctorate of Fine Arts from Knox College, would be fraud. But just saying that you have a PhD without specifying anything more specific is not.

And it comes up regularly - an easy example is the author of Men Are From Mars, Women Are From Venus.