A ticket is owned by one person, and can also belong to a team. Both are set from the ticket itself, and they are independent: a ticket can have a person, a team, both, or neither.
Set the owner
Open the ticket.
In the right panel, use the Assignee select to pick the person who owns it. The list is your workspace members.
Use the separate Team select to route it to a team, or leave it on No team.
Who gets notified
Changing the assignee notifies the new owner with an in-app and email alert that links straight to the ticket.
Changing the team does not notify anyone.
Unassigning a ticket notifies no one.
Good to know
A ticket created from a chat, or by hand, always needs an assignee to exist, so a ticket is never ownerless at the start. New teammates must be on your team before they show in the list. See Invite a team member.