Admin or Official Rep. private response setup

I have an admin or an official rep. that is creating a ticket in the system. Say it is an idea, or it could be a problem or question -- the object/type here does not matter.

The admin or official rep creates a new private ticket, because they want it to be... private. They should also be able to attach/add a user in the system to it, say John Doe.

So here is the use case for this scenario. Bill, one of our sales reps is on the phone with John Doe. Bill is logged into UR and the client, John Doe is reporting a problem with our sales module. Instead of instructing John Doe to go to the site and create a ticket, Bill simply creates it himself, sets it to Private, and then adds John Doe.

This way the problem/bug is logged, we are going to know who had the issue, and allow us to follow up with them in the future.