A ticket with a name on it gets worked. Assign from the ticket, or across a selection from the list.

Who can be assigned

The support team — the people marked as active support members for your organisation. Somebody missing from the list has not been added there, which is a setting rather than a permission problem.

Unassigned is where tickets die

Handing one over

1. Write an internal note saying where you got to and what you would try next.
2. Reassign it.
3. Mention the new owner in the note so they are actually told.

Reassigning on its own is quiet. The note is the handover.