General:
* Sent
* Delivered
* Transmitted
* Deployed
* Assigned
For people:
* Sent away
* Dismissed
* Expedited
* Deployed
For tasks:
* Completed
* Finished
* Executed
* Carried out
* Handled
For messages:
* Forwarded
* Relayed
* Communicated
* Transmitted
For enemies:
* Killed
* Slain
* Eliminated
* Destroyed
To choose the most suitable synonym, consider the specific meaning of "dispatched" in your context.