Anonymity is a serious concern for punters who have anything to lose. Even those who currently don't, may think differently in three months, six months, a year, or whatever.
And the great thing is that you don't have to do a lot to maintain it.
1) Don't give prossies your real name, not even your first name. As a real obvious example, if you bumped into an indiscreet one in the street, would you rather her call you by a fake name or your real name? Or text you by your real name? Much harder to deny you know her. There is no reason to give her your real name, so why do it?
2) Don't use your real mobile. Have a punting number. This means it is far easier to screen indiscreet prossies (turn the phone off). Also you may be surprised where your real number (and, subsequently, your contact details) can be found online.
3) Fake email. As above. There is little easier than getting a separate email. Your real email, as well as usually containing your real name, will be linked to you all over the internet.
4) There is nothing to gain from giving a prossie any real details about yourself. Why do it? They do pose an anonymity risk, however, even if small.
5) Don't take items with you that, if lost, could identify yourself. Why take your drivers licence with you? They can, and do, fall out of pockets.
6) Park round the corner. A number plate can identify you. Some prossies will try and blackmail you. If they have your plate they can say they will tell the cops you tried to rob them. The cops will be duty bound to turn up at your place. Again, it's unlikely, but you don't have to park right outside her place or where she tells you, so why do it?
7) If you plan to leave negatives about prossies you should take steps to ensure she doesn't link your face with your reviews. A woman scorned and all that.
The above advice, in my opinion, covers the basics. Following it does not ruin my punting. They are tiny precautions that take seconds of my time to accomplish. You are unlikely to encounter a truly malicious prossie, but it only takes one. You are also very likely to encounter plenty of daft ones who simply lack discretion.