It doesn't sound like there's anything illegal here, in the sense of a crime, and it also doesn't sound like there's any civil liability, because no one's been damaged, just maybe some false pretenses and hurt feelings and wasted time.
Only law enforcement can press charges. Civilians can report what they think are crimes to the police, who can refer it to the DA for prosecution, if appropriate.
There's no identity theft because there's no misuse of anyone's confidential personal or financial information for commercial gain. While it may be fraud in the sense that someone was impersonating a fictitious person, people lie to each other for social (and anti-social reasons) all the time. For example, married people take off their wedding rigths and pretend they're single so they can date unsuspecting singles.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Criminal charges may be possible. It's happening all the time with many of the new digital laws. However, just because the police and prosecutors come up with new and innovative ways to charge someone, doesn't mean it's against the law. That's for the courts to decide.
Many things which should not be illegal (i.e. fake webpages, tinkering with your electronics, ect.) have been associated with things that are (i.e. online harassment, identity theft, piracy, ect.)
If the police (or the other person) actually takes them to court, call an attorney immediately.
This information is general in nature. You should not rely on this information as legal advice, as each case is unique. This information does not create an attorney-client relationship. If you are in need of legal advice concerning a particular matter, you are encouraged to contact us at your earliest convenience.
If you would like to discuss your case further, feel free to contact our office for a free initial consultation: 612-217-0077