If it doesn’t what does it do?
You mean what’s the vernacular?
“Ring” is a hold over word from when phones had bells that rang upon receiving a signal from an operator. Now it means anytime a phone makes a sound to indicate an incoming call.
If a sound isn’t made, you can just say “notify”, because chances are it creates a dialog, or flashes a light, or does something to notify you that someone is calling your phone.