Problem backing up my iPhone to my Mac, the iPhone icon does not appear in iTunes

First try a soft reset on the iPhone.

Restart your iPhone 8 or earlier or iPod touch

1. Press and hold the Top (or Side) button until the power off slider appears.
2. Drag the slider to turn your device completely off.*
3. After your device turns off, press and hold the Top (or Side) button again until you see the Apple logo.

* With iOS 11 or later, you can turn off your device by going to Settings > General> Shut Down.

_{Source: Restart your iPhone, iPad, or iPod touch}

Note that restarting the computer may also be necessary if the soft reset doesn't fix the issue.

If a soft reset and restarting the computer doesn't fix it, then you may have to do a hard reset on the device. If so, have a look at: How to erase your iPhone, iPad, or iPod touch