Understand Dropbox Sharing

I use Dropbox. I have a folder that I share with two other people who are in different locations from me. What happens if I rename a subfolder? Let's say I change it from PHOTOS to PHOTOS SQU on my desktop. Presumably, on my desktop just the name of the folder changes. But with the automatic syncing that Dropbox does will it create a NEW folder with the new name on the cloud and then sync that to everyone's desktops? Effectively duplicating the contents of the folder? That seems to be what happens. I just need to understand better how Dropbox Sharing works. Dropbox Support has been unhelpful.