Just because they have your general information, name, phone number etc is not enough evidence that a criminal act was committed. Even the act of getting a massage is not illegal however if the person doing the massage does not have a license, that person can be held responsible.
Now if the establishment documented who you saw, what kinky actions you like to perform etc.the Government may used this information to have you give testimony against the business. However unless the sex workers are going to testify against you, your defense could be they made it all up and say nothing...unless you were stupid not to pay cash.
The Government can not publish your photo in a newspaper unless you are convicted. If they did, you would be a rich man suing the Government, the newspapers, etc. Your ex wife would be just as pleased with half of the settlement.
This is why we have a Grand Jury system in the US for the Government to prove that they have reasonable evidence to allow them to bring an indictment. REMEMBER in the US you are innocent until proven quilty.