You can't distinguish between who they should or should not block based upon who might or might be. I would suggest that accounts without a person's real name on it/ is the same used on Social Media, those people sure. If someone is using some made up words or anything other than their personal name then yes block away, no question.

If you have someone's real name you have the law you can deal with versus some semi-anonymous troll just sending more and more of their friends to harass you daily. 
But those with proper names absolutely allow us to harshly criticize the powerful on Twitter etc because we put our names on it. A crucial distinction.