When you buy a no-contract phone, you have to go to their website, like Verizon, and sign up so that you can activate the phone and make your monthly payments. You don't have to give your real name, I suppose, but you need to provide an address so they can provide you with the right area code and phone number for your phone. You can probably provide a false address, too.
If you use a false name and address, they can't track you by name and address.
But if KA calls her father on a no-contract cell phone (aka "burner" phone), then they would know the cell phone number and carrier, and try to track it back with the carrier (e.g. Verizon or AT&T) and find out where and when it was purchased, and continue to track that phone number.
She could, of course, keep buying a new cell phone, but that would be expensive if she wanted a decent phone with text, good internet capacity, etc.
All JMO, based on my experience using a no-contract Samsung phone with Verizon for about the last 8 years, and only changing my phone once to upgrade to the newer Samung model, but same phone number.