If it shows 'Only team members', moving the folder to your personal Dropbox will break your membership in the folder, and you'll have only a non-shared copy of it in your personal Dropbox.If it shows 'Anyone', you can move the shared folder to your personal Dropbox without a problem.Hover over the name of the folder and click the share icon (rectangle with an up arrow).If you're the owner of a shared folder in your work Dropbox and you want to move it to your personal Dropbox, first take a look at the folder's settings: If you're the owner of the folder, ownership will be transferred to your second Dropbox account.If you move a shared folder from one Dropbox account to another, you’ll receive a notification that you’ve left the shared folder in your first Dropbox and joined the shared folder in your second Dropbox.We recommend you check with both your admin and the folder owner to see if they've set any restrictions before moving a shared folder to your other Dropbox account.If your admin or the owner of the folder has set sharing restrictions, moving a shared folder to your other Dropbox will cause you to leave the folder entirely so you'll have a non-shared copy that doesn't sync with other members' changes.

Dropbox help naming a folder