First, check your Finder Preferences. Open Mac Finder, and click on Finder from the top-left corner status menu bar. Select Preferences > General, under Show these items on the desktop, and tick the box next to External disks. Now, check if your USB storage device is showing on your Mac desktop.
If the USB flash drive is still not visible on the Mac desktop, check if it mounts in Disk Utility. Go to the Disk Utility, if the disk name is greyed out in Disk Utility, manually mount it by clicking on the "Mount" button at the upper menu bar. Now you should see the USB flash drive appear on the Mac desktop.
Problem still exist? Try using Disk Utility First Aid to repair it since the flash drive may suffer corruption. If First Aid failed to fix the USB flash drive not showing up on the Mac desktop issue, the last resort you can try is to reformat it.
But reformatting will wipe all data off the flash drive! Therefore it's recommended to recover files from the flash drive with a data recovery tool first, here we recommend iBoysoft Data Recovery - a professional USB drive data recovery software.
This intuitive macOS program can scan the corrupted/damaged flash drive and search for any lost files, then you can preview the scanned results and recover all the files you want. After successfully recovering data from a USB flash drive that's not showing up on a Mac desktop, it is time to format the USB drive on Mac. Reconnecting the flash drive again, it should show up on the Mac desktop correctly now.