If you're using an older style Cluster HAT image (if you have /etc/default/clusterctrl then you're using the new style), follow the ClusterHAT instructions.
On the Cluster HAT images there are three types of image.
cbridge - Bridges eth0 on the controller to usb0 on the nodes (Pi Zeros).
cnat - Pi Zero have network access via either WiFi or Ethernet on the controller via NAT (Network Address Translation).
pX - Node image for each Pi Zero (replace X with the Pi Zero number, p1, p2, p3, p4, etc.).
All ClusterCTRL images start out life as a "cbridge" image, they're then reconfigured on first boot to be either of the types above.
To change the type edit the cmdline.txt file in the boot partition, this can be done either on a booted system "/boot/cmdline.txt" or from another machine editing the file on the USB/SD card.
Append "init=/sbin/reconfig-clusterctrl X" to the end of the line replacing X with the type above (this must be a single line).
During the next boot the Pi will reconfigure and change the hostname to cbridge/cnat/p1/p2/p3/p4/etc.