How to append EE ID numbers on folder onto documents within said folder

New to DS CLM 🙂 - We have main folders for each employee that is named with its EEID contained on it.  We would like to be able to pull the EEID and prepend it to every document within the subfolders.  Can this be done with Smart Rules? Any suggestions are welcomed.

Current structure:

Facility Folder > Employee Folder (Name - EEID) > Multiple subfolders (named by doc type. ex: I’9, Confidential > Documents that need EEID prepended to name