Messages are automatically redirected to the right support teams with message channels so any team member from that team can access that query / message. You can also manually assign these messages to specific team members from the pre-defined groups. 

Once assigned, the message will be moved to Assigned view and the intended team member can see this message in Assigned To Me under his private views.

To manually assign a message to a team member:

Select the message. In the conversation tab, you’ll see the option Assign To: Team Member option on top.

Select it to see a dropdown list of all team members.

Choose the team member and the message will be assigned to that team member.