Throttle or twistgrip tube is as good a description as any.
You don't necessarily need a Suzuki GT tube. I bought a cheapo generic no-name plastic tube from a bike accessory shop a while back. It was a bit long so I had to cut it to length, but otherwise it fitted the thottle assembly perfectly.
If you don't lik plastic, they're also available in aluminium.
Just make sure you get one with the correct cable conifiguration - single pull, double pull, or pull/push.