Don't know the model number or what you are seeing, but for the CR1000A, you can change the name on the Device page:

I would not recommend attempting any MAC Filtering. The feature on Apple devices that prevents the actual MAC address of the device to be shared is called the Private WiFi Address and you can turn it off if you wish, but the purpose is for increased security of your devices. The options are Off, Fixed, or Rotating, and you can find more information about that here. But again, I would just not use MAC Filtering.
Use private Wi-Fi addresses on Apple devices - Apple Support
Here are the settings that should be used on routers. Specifically for the Verizon router, do not use their WiFiProtected Setup with WPA enabled.
Recommended settings for Wi-Fi routers and access points - Apple Support