It’s actually a Zero-point Energy Field Manipulator, but yeah, someone else used “Grabbity gun” and I loved it. Great homophone and entirely in line with Valve humor.

But I do believe it canonically is called Gravity gun.

Depends on context, for warfare probably a shard rifle that can be fed any metal for ammo.

For assassination, maybe a Star Wars disruptor rifle, seems useful to atomise targets.

For my daily life I don’t need much killed or destroyed, so I’d probably go for a dual use thing, like the Portal Gun, Grabbity Gun, or perhaps high level psychic powers like Babylon 5’s Jason Ironheart.