Add Server ID in Response Header

Off the top of my head I don't believe an iRule has access to an assigned node "name". You could potentially do a reverse DNS lookup of the server to get its host name, but the simplest option given that you only have 4 app servers, is to create a string-based data group. Example:

Data group "server_dg"

10.10.10.1 := server1

10.10.10.2 := server2

10.10.10.3 := server3

10.10.10.4 := server4

And an iRule something like this:

when HTTP_RESPONSE {
     HTTP::header insert SERVER_ADDRESS [class lookup [IP::server_addr] equals server_dg]
}