Private Messaging to a Team

I would like the ability for anyone in the organization to send a message to my Service Desk team, that would only be visible to the sender and the team. I want the user to select the team from the directory, and I want my Service Desk Team to all be able to all respond to messages sent to team.

Right now the only way to accomplish this is to have every employee create a message to each individual on my team.

I don't want to use a team that everyone is a member of since some communications with the Service Desk need to remain confidential.