I am trying to find a name like "perspective view" of how a camera like this is called:
It is 2d and 3d at the same time. I'm having a hard time trying to find the name.
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This is precisely a perspective view. It's a bog standard 3D perspective-view camera -- there's nothing 2D about this at all, and nothing that requires a special name to describe.
The camera is using a standard perspective projection matrix with a real frustum, and is looking into a real 3D scene. Exactly like virtually every 3D game made in the last two decades.
It looks to me like a standard 2D side-scrolling camera. It just happens to be looking into a 3D world and using perspective projection so you get that slight sense of depth. I've seen some people call this a "2D 3D camera" in shorthand, but it doesn't have a standard name.
Games like that are often termed 2.5D and therefore I may be tempted to refer to that camera as a 2.5D side scrolling camera.
Sadly this term can mean a 2D game made to give the illusion of 3D as well as a 3D game that is designed to play and/or look like a 2D game (as in the question's example). However, in both cases the camera is usually locked to a single orientation. So I may also be tempted to call it a "fixed orientation" camera instead.
Games such as Trials Evolution can also be described as 2.5D and are a slight exception to this naming. While the orientation is still fixed, it is only fixed with relation to the track which doesn't have to be fixed to a single plane.
So with all that said, I don't think there is a particularly good name for that kind of camera other than calling it a "Perspective camera with restricted degrees of freedom" or "Fixed orientation perspective camera" or maybe call it a "perspective camera" when detailing it's view type and a "side scrolling camera" when talking about it's movement.