Now renaming the machine is a multi-day thing involving configuration changes (and that assumes it's not hard coded anywhere) to a whole bunch of software; inevitably you'll miss some and it'll break. Easier not to bother.
Changing the name might imply changing references in other services that make reference to this server for the current services that are still running. It might also imply changing bookmarks in the machines of the users of the services still running on this server.
The bookmarks are a concern because many users don't know how to do anything with bookmarks other than clicking on them, so you can't depend on them understanding how to edit the URLs of these bookmarks. Yes, that's depressing.
However, let me add that if you later decide to change a name (to something sensible like you should have chosen in the first place), you are going to be amazed at the amount of pain awaiting you. No matter how easy the manuals suggest it is to change a name, you will find that lots of obscure software has rapidly accumulated which refers to that computer using that now-ugly name. It all has to be found and changed. People mailing to you from other sites have to be told. And you will have to remember that names on old backup media labels correspond to different names.