Without changes to application means you would have to do it at "the network layer". With that I mean things like DNS, rename machine etc.
If you can modify the connection string, then you can try below connection attribute. It is really meant for database mirroring, so you would have to try if it makes work in other situations:
And, of course, make sure you handle all the other things that you have to handle when you move a database from one instance to another, like scheduled jobs, logins, linked servers etc. I.e., everything that is stored outside the database and is required for the system/application to be functioning.