While using Live Listen, my calls aren't announced

Hi gnet1a2b

welcome to the Apple (user-to-user) Community!

How nice of you to try helping your Mum!

Re: "If she has live listen on, and she receives a call the live listen tunes off, the name of the caller appears on her phone screen but no audio follows from her pods or on her phone. "

When she gets a call... seems your mum may need to change the source the audio comes from

(ie: from just listening, to the phone call using the microphone and speaker instead.)

Apple support's online article: While on a call on iPhone - Apple Support

says you can:

"Adjust the audio during a call

To change the volume, press the volume buttons on the side of iPhone.

Or swipe down on the call banner, then do any of the following:

• Mute: Tap the mute button.
• Put the call on hold: Touch and hold the mute button.
• Talk handsfree: Tap the audio button, then choose an audio destination (eg: her AirPods)."

More Apple info: Hearing accessibility features in iOS - Apple Support

All the best :-)

The AirPods User Guide also has tips, including for using phone:

Set headphone accommodations for AirPods - Apple Support