When trying to change the name of the server my solution is hitting, my unstored calcs are remaining dependent on the old server name. I have tried relaunching Servoy but that didn’t solve the problem. My unstored calcs still only appear under the old server (if it’s available) or are declared missing on startup if not.
Is this a bug?
Not a bug - calcs and relationships (and possibly auto-enter settings – I forget) are scoped to the server. (You’ll notice that relationships go missing as well.) The solution is to export your solution with the old server in place, remove or rename that server, then import the solution and choose a new server when prompted.
No need to reimport 
The repository window in Developer also has ‘move’ functionality so you can repoint servoy to use all or individual tables from another server.
Keep your old server.
Set up the new server, restart Servoy developer.
Create a new release of your project/module just in case.
Repoint.
Test.
Later, get rid of old server if no longer needed.
Heh, how long has that one been in there? I like it!