I personally would not tile behind there; rather, I'd choose a color from that backsplash and paint the walls (everywhere in the kitchen, including behind the fridge) a color from within that backsplash. You could have a carpenter build a separate, but matching piece that comes down to more closely meet the top of the refrigerator (than what's there now), too. Tiling behind there seems a lot like overkill to me. I think a backsplash surrounding and placed behind the refrigerator would start to look very busy, but maybe that's just me and my minimalist aesthetic. :)

To make it work, I would put a small counter on the left side of the fridge. Then wrap the backsplash all the way round. consistantly. behind the fridge. Same matching base cabinet, counter , backsplash as rest of kitchen. The only concern is if you can do it throughout the kitchen. Wrap the back splash all the way round. Surround your self. then no one will negativly notice space behind the fridge. They will compliment.

I assume you want to be able to see the backsplash there at the top of the fridge in that opening? If so, tile the portion from just below where the fridge is to the top of the wall.

Thanks to each of you for your input. Here is one more photo showing the entire galley kitchen.

If you can .... Try extending the wine storage all the way to the ground and then tile the upper part of the wall behind the fridge, where it is visible. Or just tile the top part using the cabinet edge as a barrier.
Otherwise I think paint would be the best option.