At least in T-Mobile's customer UX, you can set this to whatever you want per line [1]. Have tested by changing line CNAM and querying with Twilio number lookup [2]. You're supposed to be honest wrt person's name, but it's honor system.

[1] https://www.t-mobile.com/support/tutorials/device/app/ios/to...

[2] https://www.twilio.com/code-exchange/lookup