Honestly, I'm not particularly careful. It's a conscious choice I've made, though. I've known for nearly two decades that I wanted to be a professional writer, and to do that, it means that your full name, likeness, and basic personal details are going to be available for public consumption. If you're not willing to put up with that, you can't be a successful writer. Also, I prefer to write nonfiction, and a lot of the subjects I'm interested in are personal ones - relationships, youth, sexuality, etc. So a lot of what I write is personal, but again, it's something I've carefully considered.
I also don't think that information like my first and last name, my face, or the town that I live in is particularly damaging. More or less everyone that's ever met me knows these things about me, and I can't think of many situations in which hiding any of those from anyone would be particularly useful, or even possible.