Managing mass SQL Server ODBC Changes when migrating to a new SQL Server

How do you manage changing out a SQL Server and updating all the clients that connect to it to point to the new server? If I have SQLSERVER1, then buy new hardware and call the new server SQLSERVER2 and migrate all the databases over I have to change the ODBC connections on all the application servers, report servers, some workstations, etc to point to the new SQL Server instance.

Is there a way to point clients at an alias or proxy that points to the real SQL Server instance so it's not necessarily to update all the clients on a change?

The easiest method should be to point all your clients to a certain DNS name when setting up connections. When you have to switch servers, you simply assign this DNS name to the new server.

In preparation for that, you could lower the TTL value for the DNS entry to a very small value so the change has a chance to propagate quickly.