I'm not sure of the legality of it, and would certainly recommend contacting HR in your company, along with googling employee rights info for your state.
I do know that when I worked in the hospital those of us that worked in the ER, and ICU had the option of just having our last initial on our name badge, we took care of overdoses, vitims of crimes, and of course the criminals that get hurt commiting those crimes.
We had to have our last name initial, and we were told we had to give our last name if asked specifically. Otherwise we were able to remain anonymous. I agree, I too have a name that when searched pull up ONLY me. That's scary stuff. But I also have to share my complete name and title in what I do these days. I do deal with some DV issues and elder abuse at times, and it does make me uneasy, but I also have a CCW, and other than my office am usually armed. I will not be a victim.