Vendors can't set Business unit metadata for Buyers under Settings>Buyers
Vendors can set Business unit metadata for Buyers under Settings>Buyers, so all projects shared by that Buyer will have that BU automatically
Projects and jobs coming from a specific Buyer can't be edited by the Vendor to add a Business unit, nor can the Buyer's Business unit (if present) ever match the Vendor's (even if they were to share a name, they'd have different IDs and belong to different organizations).
TMS: Project & job management
Add BU metadata to Buyer under Settings>Buyer