Select Organization when end user signs up

I will be onboarding a large number of registrants that will be signing up once I go live. The current way I use my organizations and groups is I have light agents that need to only monitor a specific group\organizations tickets so I have to have the end user assigned to that organization so that the light agent can see their opened ticket. Being able to select an organization from a drop-down list would make the onboarding process seamless. 

If anyone has any suggestions on work arounds or a way to make the ticket viewable to the light agent without having to have the end user assigned to an organization, the suggestions would be greatly appreciated.