Let me try to untangle this in words and a screenshot.
The folders appearing as new folders are the old folder names. The original folders with new names are still here, but the old ones are reappearing.
It says they are modified by a team member who is synced, and the modify date is several weeks ago.
I'm going to guess this is a sync issue of some kind, but I can't wrap my head around how to advise a solution.
Our team is new to SharePoint and this is one of about a thousand questions of how to get the team synced with our site documents without major issues. We are all mac users—does anyone know of a comprehensive resource on how to get everyone synced without these kinds of errors?