French term (edited): « à la sonnette »

We do also use the rather dated expression of using a 'ringer', or 'ringing through' — however, that would probably sound odd in many contemporary contexts, so I'd recommend using 'buzzer' instead here.

Of course, it may not necessarily be an actual buzzer — these days, it is probably more likely to go 'beep'. But AFAIK the term still stays the same.

In other contexts, the actual device might be referred to as a 'sounder' — but I'm not at all sure it would be called that in this specific context.

Why not try researching some multimeteres and other similar test devices that have this sort of facility, and see just what terminology is currently most widespread?