No backsplash unless you have to mop up coffee splashes on the wall every day.

Today most people eliminate the kitchen desk in favor of cabinet space or something else they find more useful.

Have you created the layout for your renovation?

When you say renovation, what are you including in your project? If you're replacing the cabinets there is no need to keep the same layout if there is a better alternative. As latifolia says, usually people eliminate the desk area altogether. I can see you are currently using the area under the desk for petfood bowls, so clearly you need to have somewhere to put them, but is this the only place they can go if you're changing everything?

I love the floating shelves. It’s a very nice touch. To update your entire kitchen backsplash I would remove the 2x2 mosaics on all the walls and replace the with an elongated subway tile such as a 3x12. There are a variety of sizes and looks out there. Stay away from the 3x6—it has been over used and the elongated sizes are more of an updated look. Some tiles are flat and can look modern. But some have undulated surfaces that reflect light really well giving it a casual, cozy look. For the desk/coffee bar area go all the way up to the floating shelves.

Describe "renovation" please.

One look at the picture you posted tells me the island should not be there.

You don't sit at the desk; it is a hideaway for a dog feeding station.

Post more pics, describe what you are doing, and note that a backsplash is the LAST detail/decision in a kitchen, whether refresh, remodel or a brand new build.

The first decision in a remodel, is the consideration of layout, function, appliance and storage placement. Every foot and inch matters.

Waht exactly are you renovating? You have a backsplash there now . I need a lot more info as to what you are doing in the space . Post that info here in a comment DO NOT start another post all things relating to this kitcehn are now dealt with here in comments.

not certain of other things that will change..that has an impact on this corner as the kitchen does not appear very large right now.....I dont think the desk is of great value....but the space can be utilized differently in your plans and we dont have info about that. For now, I would remove the desk and the counter and the few tiles on the wall..Id leave the shelves.....Id get a less expensive cart from Ikea for the coffee.... or a shabby chic stand at Habitat store etc.....get the doggie stuff out of there . Clearing away allows new vision to take hold.

No backsplash. You've made excellent use of an odd desk and corner shelves. But, it is a bit cluttered looking already and backsplash will only make it more so.

A small change: find a pet food mat the color to your floor. It will eliminate the black hole feeling on that wall.

Since there will be much less change of splash from making coffee I will say no backsplash needed.