Are you wrapping crown molding around it? You will need that vertical to attach it. The molding will cover that small piece.

We are doing crown molding on top of the cabinets but not the hood. Here’s a rendering

I did this quickly to show two styles of hood, so don't read anything into the details.

Hoods shaped like yours will typically be spaced away from the flanking cabinets as shown on the right. I think it looks best this way.

Your hood seems a bit oversized for the space.

I would suggest a different shape shown on the left, where the sides (and I'm only talking about the sides, not the front or height etc.) are flat against the flanking cabinets.

Too late now, but I like a hood to be wider than the cooking surface, usually by 6" (3" per side).

Yeah this is helpful. Hindsight is 20/20. Given it’s already been ordered, I think we should just trim the 3 inch chimney off and raise the hood directly to the ceiling

A hood needs to be a certain height above the cooktop to function effectively.

You need to check the specs for the hood to ensure that you will still be the proper distance from the cooktop.

Leave it like it is (as long as it is the proper distance above the cooking surface.)

The shape is not helping one bit. Those little slivers of open space dust catchers are all wrong. When you do a hood that touches the adjacent cabinets, there should be no open space. No taper. That is poor design. Close in the whole, and actually integrate it into cabinet run properly, with crown across the whole. The hood is also too narrow in width.

You need to redesign to make sure there is a minimum 30” vertical clearance from the cooking zone, with the hood 6” wider than the cooking zone, without the taper. .