Please check the group with which the ticket is associated, and make sure the agent is part of that group. If the agent isn't part of the group, their name won't be listed under the ticket properties.
Kindly navigate to Admin -> Team -> Agents and click on edit next to the concerned agent's name and associate this group as well with the agent. If the agent needs to see all the tickets irrespective of the group associated with them, please grant global access to that agent so that one could see all the new tickets coming into the system.