When does the requester field show in a ticket?
The requester ticket field only shows up explicitly during two events. The first is when you create a new empty ticket, using the + Add > Ticket option. When the blank ticket pops up, a requester has to be set on the ticket and a blank requester field will display.
Once the ticket has been submitted, the requester field will disappear from the lefthand side because that information has been set.
The second instance would occur when you need to update the ticket requester and organization on the ticket. Under the subject line in the ticket, you can select (change) for the requester field to display. This will allow you to change the requester of a ticket, for more information on this see Updating ticket requesters and organizations.