Any category $\mathcal C$ with finite limits and finite colimits can be seen as a model category where the weak equivalences are the isomorphisms, and the fibrations and cofibrations are all maps.
The nlab called it the trivial model structure on $\mathcal C$. But trivial is already overloaded, especially in model categories (with trivial cofibrations, trivial fibrations). Another name that could fit is discrete as in such a category homotopy is equality: the spaces deduced from the hom-sets of the model category are discrete. But again, discrete already denotes a set seen as a category; in particular discrete model category is ambiguous.
Is there any other established name for this model structure?