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
  
  
  Press and hold the Top (or Side) button until the power off slider appears.
  Drag the slider to turn your device completely off.*
  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