Hi Vim,
The simplest and most commonly used cookie persistence is cookie insert persistence with no timeout. With this profile added to a virtual server, LTM will insert its own cookie into responses whenever a load balancing decision is made. The cookie value is an encoding of the pool name and pool member IP and port. If you want to hide the pool name and/or IP:port, you can customize the cookie insert profile's cookie name. You can also configure a custom HTTP profile with the custom persistence cookie name set in the HTTP profile field for cookies to encrypt.
It's generally a best practice to use a custom OneConnect profile with cookie persistence. If you're using SNAT on the VS, you can use a OneConnect profile source mask of 0.0.0.0. If you're not using SNAT, then set the OC source mask to 255.255.255.255.
For details on this, you can check the LTM config guide on AskF5 for your version. I can post a sample config in a bit, if you want.
Aaron