voiceover announcing caller ID to the world

VoiceOver has done this as long as I can remember. If you don't want it announcing things to the world, why not turn off speech or turn down the volume? I've been keeping speech off for years, it's just reflexive by this point. Nobody likes a phone that won't shut up.

On my phone the voice over voice is always off when I am not using it. when someone calls, I first stop the ringing by using the volume buttons, then I move the volume down and then I turn speech on so VoiceOver announces discreetly the callers ID. even better I put on my AirPods and then turn on speech.
This is never an issue for me and I don’t believe there are privacy issues. after all, it is your decision to leave speech on at all times. That’s why Apple has introduced the three finger double tap. It’s very easy and quick to use. Just make it a habit.

Try these two things and see if they make a difference. I have both set but honestly cannot remember which specifically solves your issue.
1. Go into Settings
2. Go into Accessibility
3. Go into VoiceOver
4. Go into Verbosity
5. Toggle Always Speak Notifications to Off

Alternatively, try this.

1. Go into Settings
2. Go into Phone
3. Go into Announce Calls
4. Choose never or headphones only

I'm not sure about leaving the announcements on but having them at a lower volume.

The higher the ring volume is, the louder the VO would be, over and above the VO volume set otherwise. So, try setting the ring volume from sound settings at the level where the ring is not too low to be missed, and VO is not too loud to be noticed. For me, setting it to 60 per cent or so works as I expect. HTH.

I believe as described in the previous comment, that you can set VO to never speak Call ID info, but I haven't adjusted this setting because sometimes I need to know who's calling me so it's easiest for me to simply turn the speech off and then back on if I need to hear it. I don't like having to adjust settings all the time. That's just me. ′Smile′

In fact, I have the same trouble as you. Although several posts above have given methods, such as temporarily muting VoiceOver, I always feel that this is not a good way.If you have to think about tapping twice with three fingers to switch the mute state every time, it's really too much trouble.I've told the VoiceOver development team many times that they want to add a switch in the VoiceOver settings, but so far it hasn't happened.Those around me who use third-party Android screen readers basically have the option of whether to automatically read incoming calls, so I think it is not difficult for VoiceOver to add this option.Hopefully this option will be added in the future.

I want VoiceOver to tell me who's calling or texting, obviously. But I agree it's embarrassing to broadcast that to everyone in a five meter radius.

I have the speaking rate set high enough that most people hear the caller ID or text message as gibberish. Obviously this isn't foolproof.

For years, my solution for this issue has been to use headphones or a Bluetooth headset. Not only does this give me privacy for incoming calls, but most people don't want to hear my phone yammering away while I'm using it. Along the same lines, thank you @Marc for the suggestion of having VoiceOver announce calls to headphones only.

Hey, do you turn speech off when entering passcodes? Is that really your ingenious solution? Why is VoiceOver muted when entering passwords? Though it'd also be great if we were able to toggle speaking of passwords. Those posting that weird suggestion also do use VoiceOver, right? Your comments sound like from some unskilled guy from a company's support team who knows nothing about the mentioned problem, and then just finds some piece of info in a help article and pastes it into the e-mail, one of those typical replies that we get when we report a problem. You can find workarounds in many situations, but you can't tell those posting here to develop habits that would help them avoid the problems instead of suggesting Apple should implement a permanent solution. Why is it always us who has to adapt to the conditions as they are? If this is what you prefer then so be it, but you can't request others to do so as well.

I think most of us want to know who is calling. And if your volume is just loud enough for you, the "whole world" would never know.

Those who are saying the whole world attitude, listen for a moment. A few years back, any notification was broadcasted at 100% in your ear as you were on a call. People bitched, Apple turned down the sound a little. Now go to settings sound, either alert or ringtones. Now pick any one, even if it's just your normal one. Turn your volume, on the phone to it's max. Press the button to play the sound. No big deal, right? Turn off voice over and touch that spot again. the volume at least is about 25% louder. My point in doing this is that when a call comes in, Apple acts as though voice over is not active, thereby ringing at 100% volume. Personally, I hate the fact they duck down the volume on sounds, or at least let the end user decide what is right. But if you are embarrassed by the sound? Just remember the morons who walk around on speaker. god I wanna smack them.