" I know I don't want the standard 4" chunk on the wall. "

Appears you have a 2" +/- chunk backsplash already.

This is not my kitchen, just a photo I found on houzz to describe what I am looking for - is there a certain name for it or is it just 2'?

I've lost my ability to search old Design Dilemma threads with any success. You are describing a "short" backsplash made of the counter material. It never seems to have gone out of style overseas, from my interweb forays anyways and I was looking for the Houzz thread where we discussed its seemingly renewed popularity. There is no "preferred" height that I can see. 4" has been the standard, but you can find examples shorter and taller. (Houzz posters hate tiles combined with a short counter material but I see examples of that style on, say, remodelista's page, where the last photo is from.)

@s m thank you! Your personal photo is what I have planned right now, behind the sink and the sill, and what I am picturing/considering is if that bottom trim of the beadboard was soapstone, too. (cute cat, too!)

@barncatz Your last photo is pretty much exactly what I am thinking of! I must just not have been searching the right terms.

Does anyone have this low backsplash and have any raves or regrets?

" is there a certain name for it or is it just 2'? "

2" Backsplash.

@millworkman Maybe I've read too much on counters where every edge profile has a specific name that I thought the backsplash piece would have a name, too! 😂

We had a 2" backsplash in one rental kitchen--even behind the sink. It was great. If your wall has a good scrubbable semi-gloss paint, you really don't need anything more. Even behind the cooktop, although a taller backsplash there is definitely nice to have.

Barncatz. Do you know where I could find that linear globe pendant light in the first picture you posted? The one with the black counter and wood cabinets?