Can this rear wheel be straightened or does it need to be replaced? This happened on a month old hybrid bike with 350km on it. I unluckily got the back wheel stuck in a grille when getting off a sidewalk. The wheel now wobbles a lot and keeps hitting the rear V-brakes on each rotation. The damage is isolated to this small region and I was wondering if this wheel could be straightened out, as opposed to replacing it.
That rim is dead.  You need to replace the rim at least.

Being Aluminium it won't straighten, it will crack if you un-bend it.

If you choose to continue riding it then you may get more punctures, and you will be damaging the rear brake pad with every revolution./

If the tube/tyre is still holding air then they're probably ok to reuse.