You can see which agents are active for your department by visiting the Who's Online page.
Navigate to the Admin Console:
All Live Chat users with access to more than one department will have a roll-up of all users, presented as a global statistic. Active agents will be identified with a green dot next to their name. Inactive agents will be identified with an orange dot next to their name. Each user can scroll to view all agents with access to Live Chat Support within their department.