For this you could use:
docker tag server:latest myname/server:latest
docker tag d583c3ac45fd myname/server:latest
Tags are the aliases for the full image name (d583c3ac45fd...).
So you can have as many of them associated with the same image as you like. You can remove the old name after you've re-tagged it:
docker rmi server
That will just remove the alias/tag. Since d583c3ac45fd has other names, the actual image won't be deleted.