You'll be able to easily tell which user or users is assigned to any customer from the customers page.
First select a customer from within a segment or by using the Search bar at the top of the app.
Once you've selected a customer, you'll be able to see the users assigned. Hover the mouse over the letter to see their full name.
To see the assigned users that cannot fit the screen, click __+users in the same field for a full list of everybody assigned.