Internal vs External request tagging

You can add a header or cookie in several ways. Depending on your BIG-IP software version, you may be able to customize an HTTP profile with the "Request Header Insert" option, or insert a cookie or header in an LTM Traffic Policy, or use an iRule to do the same thing.

You're on your own when configuring the single downstream server, since it'll depend on which of the above options you chose.