SQL Server Migration Plan - Alias Options for Multiple Apps Connecting
you may eventually rename the old VM and the old instance (es: prdServer01_old) and assign the prodServer01 at the new one (both VM and instance)
prdServer01 --&gt; prdServer01_old
prdServer02 --&gt; prdServer01
here how to rename an instance:
https://docs.microsoft.com/en-us/sql/database-engine/install-windows/rename-a-computer-that-hosts-a-stand-alone-instance-of-sql-server?view=sql-server-ver15
As i'm supposing you are not using ip addresses in connection string, that's all.