The agent who creates the task should assign the owner to it. However, you can re-assign tasks to yourself or other agents when required. Please, note that tasks can also be assigned through automation rules like workflows and macros.
To re-assign tasks:
Click the [Module]Tab from the top bar. (E.g., Tickets, Tasks, etc.)
Select Tasks from the modules menu.
In the Task Details page, click the Task Owner field.