I'm often surprised when someone will paste a screenshot of a tweet with the name blurred (presumably to protect them from harassment). The contents of the tweet are easily searchable...
Public tweets are a different scenario, they are things that have intentionally been shouted out into the void for anyone to hear. Blurring out names is a courtesy to prevent low-effort harrassment (which is most of it), while using the tweet for its intended purpose (i.e. showing its message to the public).
