I have a one handle bathroom sink. Underneath the sink, under the escutcheon, there is a small leak of water coming out of the middle hole. It is the same hole that the stopper plug rod goes up into. It's the hole between the hot and cold water line connections. Where is this leak coming from and how can it be fixed exactly? What is the name of this hole/outlet?

Your leak will be coming from one of two places. There could be a crack in the valve body or the water could be seeping past the seal between the valve and the lavatory. The hole the stopper rod fits through has no name and is simply a chase through the chrome valve cover. It has no connection to the water. If you can pinpoint the source of the leak we can tell you how to go about repairing it. Good luck, Tom