Dynatrace Sever name is basically your Server Host Name.
So just change the host name and restart the server and then launch your Dynatrace client to see whether name has been changed or not.
An alternate way to perform this task without having to rename your server is to perform the following steps:
1) Shutdown your AppMon Server
2) Edit SERVER_HOME/server/conf/server.config.xml
3) Change the NAME= attribute in the <server> block. This will currently be set to your hostname. Any string is valid.
4) Save the file, restart your AppMon Server.
5) Note the new name in the Client Cockpit.