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 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.
Note: When manually assigning an agent to a ticket, ensure you select the appropriate group first, followed by the agent. If the group is not selected and you attempt to change the agent, the changes will not be reflected in the ticket. The same principle applies when setting up an automation: if a ticket needs to be assigned to a new agent, first select the target group, then the agent.