The bed is really much too narrow to plant anything other than a low groundcover, though you might set up a trellis and plant a twining vine that won't get overgrown. Even then, in order to get the trellis off the house itself, it will be difficult to get enough distance from the house and still have room for the vine.

I agree that the space is very tight. Unless you are looking at something that has a very narrow, columnar habit, a characteristic that is going to eliminate most natives.

Ilex crenata 'Sky Pencil' will fit the space - plant only gets about 18" in diameter, max. and can grow 6-8' tall (perhaps taller under good conditions). Also quite shade tolerant (appears to be a fair amount of shade here) and is evergreen.

Ive seen trees planted that close but what it does it leans forward towards the light or because the wind flow pushes them out. So bear that in mind when you plant too closely to the house. There are many columnar trees that may fit the bill. I've seen one thats a columnar oak tree. or a nice weeping copper beech. or maybe because you have nice gunmetal grey home, a birch (only thing though some birches are prone to disease).

A trellis with something growing on it?