Stars are a personal organization system in your helpdesk. So when other Agents set Stars on tickets you won’t be able to see them, and likewise when you set Stars on tickets they are not visible to other Agents in the helpdesk.
If you need a shared way of marking tickets in the helpdesk, it would be best to use Labels or Urgency as these are globally visible and can be shared between Agents.
You can also use Stars as a filter on your tickets and rename them to fit your needs:
For more information about personalizing My Stars check out the Agent Guide.