The 'clusterName' JSON key is used to associate BIG-IP devices that are part of the same DSC cluster. This is an optional field that a user can provide when establishing device-trust with the BIG-IQ:
API Reference: BIG-IQ Device Trust
Establish trust between a BIG-IQ Centralized Management system and a BIG-IP device
eg. curl -sku admin:changeme -X POST -H "content-type: application/json" -d @bigiq-device-trust.json | json_pp
cat bigiq-device-trust.json
{
"address": "10.154.170.20",
"clusterName": "test-v11-5", <<<<<<<< you can enter one of your choosing
"password": "changeme",
"useBigiqSync": false,
"userName": "admin"
}