This is a rare problem that we have heard reported before. I say rare because using real, full names as display names is not that common but does come up. Like I use just my first name and there are a lot of people named Charles in the world so I would not consider it PII for the purposes of GDPR.
Unfortunately we do not yet have a good solution as "quoted content" is almost the same as someone copy/pasting the post into their own editor and replying with it. The only real way to address this is a full database search and replace which is, as you might expect, intensive. It is also prone to errors as let's say someone's name on your community if John Doe. We remove all quoted post references but then elsewhere someone was talking about John Doe in their own post. That's not PII as it's not attributed to the user but would get replaced and break a conversation.