Question regarding Excel connection to SSAS cube
Easiest fix would be to have your networking folks point DNS for your old server name to your new server's IP address. Unless you rely on Kerberos that will likely work fine.

If that's not an option, then if you left click on the PivotTable, to the Data tab in the ribbon, then click Properties under the Connections section, then go to the Definition tab, please see if "Always use connection file" is checked. If it is, then you can just manually edit the .odc file in Notepad and point to the new server.

If "Always use connection file" isn't checked, then you can left click on the PivotTable, then go to the PivotTable Tools... Analyze tab in the ribbon, then click the Change Data Source button, then click Choose Connection, then choose a different .odc file to connect to. Your PivotTables should be preserved and they should now connect to your new server.