WiFi - under connected devices my iPhone is just listed as "iPhone" whereas it has a unique name in the iPhone settings>general>about>name.
I have tried rebooting the Spectrum Technicolor modem as well as my iPhone.
Is there any way to edit this name so it shows up as the unique name I want it to have in my modem (in the connected devices list)?
This sounds like a question for the experts at the Apple store to answer. I don't believe the Technicolor gateway allows you to create an 'alias' for the device name that is being broadcast by the phone. If you still need a more definitive answer, please provide the exact model of the Technicolor modem (they make several) and your ZIP Code.
I have reviewed the TC8717 manual and can confirm there is no option to change the displayed name of a wireless device connected to the WiFi. You can only edit the SSID network name optionally being broadcast by your router on the WiFi channels. Even that possibility is limited to editing only two characters of the SSID.
If it is possible to change something in your iPhone to get a more detailed name display, the experts at your local Apple store should be able to help you. You can also try asking on a Technicolor forum - Google is your friend.