I had the same trouble as some other folks on this issue.
Sorry if this is obvious but, 2 things:
1) Make sure you use the cable that came with the drive - others may seem to fit with drive, but may not work.
2) Nothing shows up on the desktop until you insert a disc.
iMac 21.5″, macOS 10.15
1) That is true, there are two different types of mini USB connectors.
My LG Slim DVD/CD drive SP80NB80 has the Mini-A type USB connector.
2) That is correct, the DVD or CD is what shows up on the desktop, not the LG drive.
To see the empty LG drive, go to Apple > About This Mac > System Report... and select USB in the Hardware section.
If you are having trouble with your LG Slim DVD/CD drive.
1) Test some different DVDs/CDs in the LG drive.
2) Test the LG drive plugged into a different Mac or PC.
1) That is true, there are two different types of mini USB connectors.
My LG Slim DVD/CD drive SP80NB80 has the Mini-A type USB connector.
2) That is correct, the DVD or CD is what shows up on the desktop, not the LG drive.
To see the empty LG drive, go to Apple > About This Mac > System Report... and select USB in the Hardware section.
If you are having trouble with your LG Slim DVD/CD drive.
1) Test some different DVDs/CDs in the LG drive.
2) Test the LG drive plugged into a different Mac or PC.
That nothing shows up until a disc is inserted is normal operation. My 2020 27" iMac running Monterey does exactly the same thing, it is no bother what so ever.
LG Ultra Slim DVD drive not working with iMac 21.5"
