How Do I Know if a Customer is Mine?

In your question list under the Ask tab, each question is labeled with the customer name and the librarian. 

If the customer is affiliated with another library, the name is listed underneath the Patron field. If no library is listed, the customer is yours. Also, the green up arrow in the right-hand column means it was your customer, the orange down arrow means one of your providers assisted a different library's customer.

Within the transcript, you can check the referring URL (the last page the customer was on when they entered the service) or the Referred To or Referred By in the yellow box across the top.

Referred To means that the customer is yours, but was picked up by a librarian from the listed library:

 

Referred By means one of your librarians picked up a chat with a customer from the listed library: