The worst is probably having a somewhat unusual name that overlaps with a notorious person who could at least plausibly (especially to somewhat off-kilter randos) possibly be you.
I went to school with someone who shared a name with an individual who is in a high-profile public legal spat in NY involving another high-profile NY personality. (Not going to say who or you can figure out the name with modest Google-fu.) My classmate got various death threats etc.
Ever seen The Big Lebowski?
Ironically, being relatively faceless has burned me as well. I have a fairly common name, so when someone else with the same name made a shitty comment on some board on Facebook, I had days of being attacked, getting DMd to kill myself, brutal comments on all my posts...it was hours and days of cleanup and banning people.