Let $R$ be a graded ring endowed with a graded derivation $d \colon R \rightarrow R$ of degree $k$. Let $M$ be a graded $R$-module. Is there a standard name for degree $k$ maps $\mu \colon M \rightarrow M$ which satisfy a graded Leibniz rule with respect to $d$? That is, maps which satisfy $$ \mu \left( r \cdot m \right) = dr \cdot m + (-1)^{k \cdot \left| r \right|} r \cdot \mu \left( m \right). $$ When $k=1, d^2 = 0$ and $\mu^2 = 0$ then this compatibility is precisely what is required to endow $M$ with a structure of a DG-module over $(R,d)$ but I'm interested in the more general case but even then, I only found references that treat the pair $\left( M, \mu \right)$ and not the map $\mu$ seperately.
It seems tempting to call such maps "module derivations on $M$ over $d$" or something like that but googling module derivations gives me mostly things of the form $R \rightarrow M$ where $R$ is a ring and $M$ is a bimodule and not of the form $M \rightarrow M$.