It would be best to paint the walls a color which shows off the surfaces to their best advantage rather then a color that is on trend. Grays are the on trend color now, but it is very difficult to get warm wood tones to work well with cool gray tones. The result can be rather drab. That is why the grays are usually paired with white or dark cabinetry.

In general, warm wood tones look best with cream, creamy beige and blues and greens. The blues and greens can have gray undertones, but they tend to darken rooms when they do - not always.

Here is an article about possible grays - most of these actually read blue or green:

http://www.housekaboodle.com/gray-paint-colors-with-wood-trim/

In the picture, your wood cabinets, white trim and floors all read "warm." I would go with a cream backsplash and possibly a creamy beige wall color to keep the kitchen bright and warm and inviting. If you like more color, consider a color from the article above - but not one that makes your cabinets look yellow.

This one, especially with the addition of the white / cream, is very pretty:

While gray is popular, there are many on this forum who have said they are tired of it - especially when used in the wrong situation and in colder climates.

I have wood cabinets and this is my backsplash:

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~57088087