So the consequence of the geometrization (according to 3-manifold group note) is that any finite-volumed hyperbolic 3-manifold is residually finite. So the question is:

Q1. If $M$ is an infinite-volumed hyperbolic 3-manifold, in particular, a compact 3-manifold whose interior admits a hyperbolic structure such that it contains at least one boundary component with genus $\geq 2$, then $\pi_1(M)$ is residually finite?

Since any subgroup of a residually finite group is again residually finite, I can also ask:

Q2. Any infinite-volumed hyperbolic 3-manifold is a covering of a finite-volumed hyperbolic 3-manifold? i.e., if $M = \Bbb H^3/\Gamma$ is infinite-volumed, then I can find $\tilde{\Gamma}>\Gamma$ such that $\Bbb H^3/\tilde{\Gamma}$ is finite-volumed?

I think the first question is positive but couldn't find a reason.

Edit: I think this answer answers Q1 but I'm not sure if it's dealing with my case (infinite volumed case) because I think the main reference of that is 3-manifold groups note and I think that note mainly deals with finite volumed ones.