ServiceDesk is not a true multi-tenanted solution sorry.
You could customise to get SD only showing just the tickets appropriate to each support group but you're always running the risk that a poorly written workflow, report or mistake with permissions could allow one team to see tickets for another.
It really depends on how separated you need your teams and tickets to be.
You'd also want to consider whether any customisations you apply would be able to be implemented in 7.5 as this has core workflows that are not supposed to be modified.