Do I need an exhaust hole near my sink?
Yes, you need that - it's plumbing code in most areas. It's an air vent which prevents forming a siphon from the sink into the dishwasher.

The most widely used term seems to be "Air Gap" though you will get better results with "dishwasher air gap"

https://en.wikipedia.org/wiki/Air_gap_(plumbing)

If you remodeled your kitchen to provide a dedicated, vented in the wall, drain for the dishwasher, you would not need it, as the vent in the wall would serve the same purpose.