Once the Super Hornets came on the scene, the "Hornet Demo" was already a thing so to differentiate from that they called themselves the Rhino Demo Teams since Rhino is the nickname for the Super Hornet in the same way that F-16s are called Vipers. The Navy just seems to be a lot less formal than the Air Force so I suspect this name came from the crews more than anything. The name "East/West Coast Super Hornet Demonstration Team" was the more formal version but meant the same thing.
Then the Legacy Hornets went away, VFA-122 got out of doing full demos, and the Navy really gave up on performances for a while.
When the Navy got back into airshows more in 2019, it added some other units (EA-18Gs, T-6Bs, T-45s) to the mix for extra variety and to distribute the pressure of supporting events in addition to normal operations. VFA-122 was part of this expansion with their Super Hornets, but they did not regain 'demo team' status.
Where it stands today is that we have two 'full' demonstration teams:
- F-18 Super Hornet Demo Team (aka the Rhino Demo Team) on the East Coast (VFA-106)
- F-35C Lightning II Demo Team on the West Coast (VFA-125)
- F-18 Super Hornets from VFA-122
- EA-18G Growlers from VAQ-129 (sometimes called the Growler Demo Team even though they do not fly a 'full' demo)
- T-6 Texan IIs from ???
- T-45 Goshawks from ???