Will renaming a shared file or folder also rename it in everyone else's Dropbox folder?

As it isnt mentioned in any of the materials that have come out with it I think we can probably safely assume that no it won't. 

First, remember that share links and shared folders work very differently.

If you rename a file or folder that you've created a link to, anyone accessing that link will see the new name. Share links do not sync to other users, so nothing will be renamed on their local computers. If they had previously downloaded the content before you renamed it, they will not see the change.

A shared folder on the other hand does sync to any member of the share. Any changes made inside the shared folder will sync to all other members. Rename a file or sub-folder within the share and they will have their copy renamed to match. The exception here is if you were to rename the shared folder itself. Any member of a shared folder can rename the folder without affecting any other member.

For instance... I create a folder called John and invite you to it. You accept and the John folder is synced to your account. A folder called John isn't very descriptive to you so you rename it to Rich. Only you will see the new name, but the folder will continue to work for everyone. You can also move the folder within your Dropbox without affecting any other member.

Related to that (but not to your question), if you share a folder and later rename it, any new members you share it with will still see the original name. So I create a folder called John and share it with you. I later rename it to Project and invite others to it. They accept and will receive a folder called John.

We are using Dropbox for Business and share files.  We do not use Teams. We are on Windows 10.

Our "rename" seems to be working differently all of the sudden.  We had a shared folder called CUSTOMERS with thousands of sub-folders and files in it.  I don't like my folder names to have all caps so I renamed my CUSTOMERS to Customers.  Everyone else that shared that folder with me now have the folders CUSTOMERS and Customers.  It appeared to be moving all folders/files from CUSTOMERS to Customers.  All folders and files were then downloaded to each user's laptop. This took hours for some users. The CUSTOMERS file is now empty in everyone's dropbox and all sub-folders/files are in Customers.  I thought that shouldn't happen.  Can anyone explain what's going on?  Thanks.

I'd love to see Dropbox answer this type of thing. I have issues like this and its very confusing. 

I face the same issue.

I'm the owner of the master folder which holds over 40,000 files and once I have renamed the folder, suddenly all files are under sync icon and I'm receicing notification that folders are being removed. What will happen to all files? Will editors with whom it has been shared will have double files on their dropbox or do I need to share again the renamed folder?

This is very unpleasant user experience just for renaming a folder.....  

You need to understand how Dropbox sees things. A rename of a file or folder is seen as a deletion of the old and an addition of the new. Dropbox sees that Folder1 no longer exists and that Folder2 does. It can only assume that one has been deleted and the other added. As it's indexing the files in the "new" folder it will determine that the content is the same as data that's already in the account and will only upload and download any changes that it sees. When the indexing and syncing is complete, Dropbox will see that the folder was shared and reconnect you to it. Just be patient and allow Dropbox to work it all out. If it's a large folder, this will take time.

The other members of the shared folder shouldn't notice a thing. Renaming a shraed folder only affects the person renaming it. You can move and/or rename your shared folder to anything and the name and location will stay the same for all other members. Also, anyone you invite to your renamed folder in the future will still receive the folder with the original name.