Does a vector field associated to a vector field $X$ via the Ricci curvature and the metric have a name?

Question

Let $(M,g)$ be a Riemannian manifold, and let $X \in \Gamma(TM)$. There is a unique vector field $\tilde X$ on $M$, satisfying $ \text{Ric}(X,V)=g(\tilde X,V)$ for every vector field $V \in \Gamma(TM).$

Let us call $\tilde X$ the associated vector field to $X$ (via Ricci and the metric).

Does this $\tilde X$ have an accepted name?