No one is anonymous on a radio transmitter. People think they are anonymous and some of them are prosecuted nearly every month. People even go on the police bands to play around and taunt the police. They are not anonymous and they get caught routinely.
Here is how it works. Many repeaters have what they call ‘radio fingerprinting’. When you use a repeater, you key-up your radio and then give your call sign. The control operator at the repeater logs the user’s call sign and links it to your radio’s unique repeater input signal in their database. I have seen this demonstrated. The oscillator start-up image of two radios is never the same. For a small fraction of a second as the oscillator in the radio struggles to reach its frequency, it creates a unique waveform as seen on something like an oscilloscope. It’s the same every time on the same radio and never the same from one radio to the next. So a week after saying “ha ha ha, you can’t catch me” on the police frequencies, there is a police investigator with a copy of your radio’s unique oscillator start-up image, inquiring with it to the local amateur radio repeater owners. The repeater owners give the call sign of the matching image to the police, who give it to the FCC. I saw this technology demonstrated once at a ham fest. Every time I keyed-up my handheld radio, the resulting image was the same. Several people did it there and no two of the images from different radios were ever the same. I was even once locked-out of a repeater for “kerchunking” without identifying. After being locked out, the repeater simply wouldn’t respond in any way to my input signal. When I called the repeater owner to ask why I couldn’t get in to the repeater, he said I was locked out for kerchunking and agreed to unlock it for me if I promised not to do it again. I gave him my call sign and he unlocked it for me. Kerchunking is when you key-up the radio to see if you can open the repeater squelch (usually at a significant distance from the repeater to test the range of your radio) without giving your call sign.