Within Teamwork Desk, you can notify another
agent of a specific ticket by mentioning them
in a note.
When viewing a ticket, go to the Note tab.

From here, you can then then add a note to
the agent you wish and notify them by typing
@ followed by
their name. 
Any users who have been added to your
Teamwork Desk site as agents can be
@mentioned. Once you use the
@ symbol and
type a letter after it the names relating to
that letter will be populated into a list. - The dropdown list will include any agents
with permission to access the inbox, along
with any administrators on the site.
Note: Only users who have accepted
their Teamwork Desk invitation can be
notified.
For more information, see: Adding a Note to a
Ticket