I think it'd be hard from a screen name, unless they were truly digging and could hack and get your IP number. From there, I guess if they tried hard enough, they could get information. I'd think it wouldn't be easy.
I try not to give out a ton of info online, as far as message boards. My first name, and my state, and that's about it. I rarely, if ever, post my town, and I never post my address. A couple people I know have my cell phone number. I'm not a paranoid person, just an overly... nervous one, so I'm particular and watchful of the information I give out.
On the other hand, I have friends that go online, and give out all their info publicly, and really don't see a problem with it.
Now... with that said...
Once upon a time, I was on another forum. Between my first name, and me slipping the name of one of the rescues I volunteer with and my vet clinic, someone who is a complete nut job that hated me, got in contact with not only my rescue, but other rescues I'm with, and my vet clinic. They tried prying info out of them on if I really owned the dogs I said I did, were they really speutered, and then threatened to call the SPCA and have me investigated for animal neglect for the amount of animals I owned, and to have me investigated to see if my animals were stolen. Yeah, they needed some serious medication.
They were a complete NUT JOB. I never saw the SPCA, but I was alerted quickly by my rescues and my vet that a whack job was trying to get info out of them. Never found out 100% for a fact who it was, but I have a very, very, very, VERY good idea, and a good amount of proof who it was.
Anyways, I think it'd be nearly impossible to find out who you are without posting any info such as a last name, address, phone number, ect.
