Say I'm working with client A and client B. I want to keep notifications on, but if I'm presenting my screen to client A, I don't really care that they can see my Slack notifications, but I do care that they can see that the notification comes from a channel named after Client B.
Is there a way to prevent this while still having notifications on?
I don't think there is a way to remove the channel name from Slack notifications. The only possible solution I could imagine is to change your channel-specific notification settings or mute all other channels for the duration of your screen sharing sessions. When you mute a channel, you don't receive notifications, but for all @mentions, you get a notification bubble in front of the channel names.
