supplier definition level the combination of site name + procurement BU is unique

We need investigate please if at supplier definition level the combination of site name + procurement BU is unique which I believe is true. Meaning that if for a supplier site we want to use it for US1 BU and US2 BU at the same time for procurement then we need to open two different sites. Can we do with same name ? in EBS the concept is different , you just open a site and provide it access for unlimited number of BUS us (no need to open sites per BU).