Turns out when I ran SELECT @@SERVERNAME , it was returning the OLD name.
The fix was to run this script (found here):
-- Use the Master database
USE master
GO
-- Declare local variables
DECLARE @serverproperty_servername varchar(100),
@servername varchar(100)
-- Get the value returned by the SERVERPROPERTY system function
SELECT @serverproperty_servername = CONVERT(varchar(100), SERVERPROPERTY('ServerName'))
-- Get the value returned by @@SERVERNAME global variable
SELECT @servername = CONVERT(varchar(100), @@SERVERNAME)
-- Drop the server with incorrect name
EXEC sp_dropserver @server=@servername
-- Add the correct server as a local server
EXEC sp_addserver @server=@serverproperty_servername, @local='local'
The server needed a reboot afterwards to make this fix work.