I don't see anything in TA's privacy policy which precludes it from providing your name to a hotel (or other travel services provider). However, because you have not provided the name of the property or the nature of the complaint, it is hard to tell, but I would generally surmise that if the property is small enough, you raised the issue directly to the property, and the issue or series of issues are sufficiently unique, e.g. you were the only person who both had inoperable air conditioning and food poisoning from room service, that the property derived your name from its records.

Either way, I can't see that the property has violated TA's privacy policy or likely its own. It would be fairly common for a hotel policy to permit the use of your name to respond to a complaint.

As a general rule, I would not post a business review without presuming that at least the business operator will have access to at least your name and contact information.