When an orbit space has finitely many symplectic leaves?

Let $V$ be a finite dimensional complex vector space and $G$ be a finite subgroup of $G<\operatorname{GL}(V)$.

My question is, essentially, when do the orbit space $V/G$ have finitely many symplectic leaves?

My interest lies, specially, in the case when $V=h \oplus h^*$, and $G$ is given by a finite subgroup $W$ of $\operatorname{GL}(h)$ acting on $V$ diagonally (with contragradiente representation on $h^*$).

This question is motived by symplectic singularities and rational Cherednik algebras. I know that the answer is positive when $V=h \oplus h^*$ and $W$ is a complex reflection group, and I am curious about the general case.