Show the image, don't worry so much about what it's called.

I don't think it's any, at least not of the classic types. Reeded should have curvy tops to each section and that looks flat. Fluted should have rounded grooves and I don't think there's enough space here for that detail. Beadboard has, well, beading, which is like a skinny strip of roundedness usually paired with a larger flat strip...

Try "slat" wood?

Nope. Not even partially close. In price or in profile.

To me it looks like pole wrap. I just read a blog post about how people are using this to mimic the reeded furniture that's in style now.

This what I think of when I think of fluted:

Ugh, I just saw this today in a moulding/trim catalog! It does have a name, and it's definitely not beadboard (nor was it called fluted/reeded in the example I saw). The catalog where I saw it offered it with several different "gap" sizes between each of the pieces. If I can find the name, I'll add it--it wasn't in the first place I thought it would be, unfortunately, so I'd have to dig through the others I looked at. But if you go to a good millwork place, they should be able to direct you to something similar.

Oh, that sounds right!!! If you do end up finding it again then please do share. I’d really appreciate it! Part of what I was trying to explain to our cabinetry vendor is that I liked that the “grooves” (or like you said, “gap” sizes) were all roughly 1/2 the side of the thin slats. They told me they “can provide individual boards 1-1/2” thick that would be installed on site over the back panel.” I’d obviously confirm that the sides are going to be done too. But I feel like that description should get the job done?? I just hope they don’t try charging an excessive amount for this.

Found it--shiplap or nickel gap wall paneling. (Not totally clear on what the difference between the two is--I was looking for unrelated trim and just stopped because I hadn't heard of nickel gap--but they are similar. The particular place whose catalog I had advertised that they prefer a 51-cents gap instead of a nickel gap because of the aesthetics...) Most have bigger panels but some are narrow or can be done custom and look like your photo. Not sure that is exactly what you're looking for but I think it would get you on the right track. Wayfair has some examples (though I would still talk with a local millwork place for a better understanding of what you're trying to get).

I think this could be an after-market add-on as long if it doesn't need to match a cabinet stain, in which case you could just have your cabinet people do a flat back there knowing that you'd add paneling.

Shiplap isn’t even the same county as fluted or reeded. Theres no curves involved. One is convex, one is concave. Curves are very expensive. Which is why it’s in the upper end designs. Fake Joanna Gaines shiplap is walmart cheap. In more ways than one.

Beadboard

There's a discussion on Houzz about a kitchen and they guy did exactly what you're looking for. Looks great. I'll try to find it and maybe you can reach out to him and find out how they did it. At least that's how I remember it, lol.

Try ribbed wall paneling or slat wood panels as search terms.

Search for "sheeted tambour" -- you may find inexpensive alternatives.

As @cawaps said, the picture is a slatwood or ribbed panel. They are widely available but can be a bit pricey.

https://www.outwater.com/search/?keyword=tambour&mpp=24

All types of wood tambour

https://www.outwater.com/search/?keyword=fluted%20wall%20cladding

I cannot tell from the photo if it has a radius. If so, we would call that reeded. If the pieces of Oak are flat, we would call this battens or a batten panel.

Nickel gap is tongue and groove flat paneling with a narrow gap so the nails are hidden.