I want to know, because to use the terms in search and so.
A "2 color design" or a "2 color design with overprint". That's unfortunately not an official term for this specific style but still close to what it is.
In printing, I would call this a "multi channel" design but that's not a search term that will help you much if you are looking for inspiration online or examples; this term is related to the technique to achieve this with spot colors in Adobe Photoshop, not the style itself. It can help you find some tutorials to prepare print-ready files though.
And for clients, unfortunately, you might need to use the term "duotone" even though it's not really a duotone as mentioned in the other answer. Or stick to multi channel and explain them what it is.