Tickets that are created always have a Requester user set as the primary owner of the ticket.
Creating a ticket on behalf of another user
You can create a ticket on behalf of another user, by changing the requester of the ticket before it is submitted. This is available from the Create a ticket dialogue.
Changing the requester on a ticket
Agents have the option to change the Requester from one user to another, when the ticket has already been sent in via a Collaboration channel.
Suptask automatically lists the users who have access to the ticket when selecting the Requester of a ticket.
For tickets in Direct Messages (DM), the users who are a part of the DM conversation will be available to set as the Requester.