The Wales international footballer was found not guilty at a retrial of raping a 19-year-old woman following a five-year battle to clear his name.
The complainant was forced to move house at least five times following the original trial, after being repeatedly identified on social media.
North Wales Police are now investigating alleged further naming of the woman in the wake of the retrial - a criminal offence under Section Five of the Sexual Offences Amendments Act. Detective Chief Inspector Jason Devonport, who is leading the investigation, said: “North Wales Police are investigating allegations under Section Five of the Sexual Offences Act, where any individual found committing these offences will be investigated and brought to justice.”
“People should be reminded that the complainant has the right to life-long anonymity.”
The striker, 27, was originally convicted of raping the woman in a Premier Inn near Rhyl, north Wales, in May 2011.
He served half of a five-year prison sentence before being released, but there was a public outcry when he attempted to return to professional football.
Mr Evans joined League One club Chesterfield FC after the Court of Appeal quashed his conviction and ordered a retrial earlier this year.
His family had employed private investigators to gather new evidence, with a £50,000 reward offered for information to help his case.
In a rare move, the jury at Cardiff Crown Court heard evidence from two men who had sex with the complainant around the time of the rape allegation.
The jury of seven women and five men took less than three hours to find Mr Evans not guilty of the charge following the eight-day trial.
After the verdict, Mr Evans said he was “overwhelmed with relief”.
Campaigners reacted angrily after Mr Evans was cleared of rape, with many voicing concerns that the case had set a dangerous precedent.