Is there a standard name for "matching" in bipartite graphs where only vertices belonging to one side have to be matched just once?

Question

Let $G=(L\cup R, E)$ be a bipartite graph (i.e. $E\subseteq L\times R$).

A $(*)$ in the graph is a set of edges $M\subseteq E$ such that every vertex in $L$ is matched in $M$ at most once (i.e. $\forall l\in L:|M\cap (\{l\}\times R)|\leq 1$).

What is the name for such set $M$? (one-side matching?)