What is the composition term for placing the subject off-center?

I'm pretty sure that it's just "subject off-center", with no special words. A Google search for that term returns a million results, and I don't see a common other term used, let alone a consensus for some other label.

However, in photography over the past century, it's pretty strongly related to the rule of thirds, which is widely understood as a suggestion to compose in exactly this way, with subjects a third of the way into the frame rather then centered. (The original "rule of thirds" was about dividing lines or blocks of color in a composition, but the idea of subject placement is very strong in its modern oft-repeated incarnation. You'll see it often in the search results above, although clearly not all off-center subjects follow the strict guideline.)

The idea that the fraction ¹⁄₃ (or any other particular ratio) is special isn't based on anything rational, but it's generally true that centered subjects tend to be more static; using an off-center subject allows use of tension and dynamic balance in composition. (More on this under When is it OK to place the subject in the middle of a picture?)