The simple answer is go to edit..settings, and fix the screen name there. You'll see that the old screen name that is appearing in that error, is being taken from what is there. So fix that and then stop and start the server and it will be fine. And if the screen name there is fine then make sure it appears on the grid in "configure server".
And infact the computer's hostname is irrelevant to synergy since it isn't used by synergy.. (Though I agree with the idea of giving the computer a useful hostname and having the screen name be the same as that!).
Synergy doesn't actually use the computer's hostname.
It uses what is called a "screen name" which is a synergy specific thing. Every computer's screen name has to be distinct. Each computer has an instance of synergy running.
A computer's / the screen name for an instance of synergy, is under "edit..settings", of the synergy window, on that computer.
And you have screen names under "configure server". The computer whose synergy instance is configured as 'server', has a "configure server" button which shows a window with the grid of screens where you drag pictures of computers onto the grid to represent the computers you want to move your mouse among. Each of those computers has to be given a screen name in that window. Including the server.
The error "FATAL unknown screen name..." happens if the screen name under edit..settings does not exist among the screen names in the configure server window.
And that makes sense, it thinks the server isn't among the group of computers on the grid!
Really synergy should give a more meaningful error message telling the user that they should ensure that the screen name in edit..settings matches the screen name of a computer on the grid. (And of course two computers on the grid can't have the same screen name, that'd give another error, albeit a warning one rather than a fatal one!).
Also I notice some answers say to edit an entry in the registry, but actually when you do edit..settings, then the registry entry with
--name that some other answers refer to, will be updated anyway.