Ecamm Live will automatically show a connected iPhone or iPad's screen as a camera source when the device is connected via USB. 

If this isn't happening, the device may need to be paired with the Mac.
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In macOS 10.15 or newer, iOS devices are managed in the Finder. Look for the device in the left-hand sidebar of any Finder window. Click it and follow the steps to Trust the device. (If you see device settings instead, it's already trusted.)

Meanwhile, on the iOS device's screen, you' may see a message as well.
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In 10.14 (Mojave), devices are managed in iTunes. Open iTunes, and click the tiny phone icon above the sidebar. Look for this message.

If the device still isn't showing up in Ecamm Live, try rebooting the Mac, and rebooting the iOS device.