Mac desktop icons not showing up

Then download and run Etrecheck. Etrecheck is a diagnostic tool that was developed by one of the most respected users here in the ASC and recommended by Apple Support  to provide a snapshot of the system and help identify the more obvious culprits that can adversely affect a Mac's performance.

Copy the report

and use the Add Text button to include the report in your reply. How to use the Add Text Feature When Posting Large Amounts of Text, i.e. an Etrecheck Report

Before running Etrecheck assign Full Disk Access to Etrecheck so that it can get additional information from the Console and log files for the report:

Then we can examine the report and see if we can determine what's causing the problem..

Did you restart your mac?

If it is not enough, check to see if the desktop items show up normally whilst in Safe Mode (this is slow, that is normal).

If you log in to a different user account, do things appear normally on the desktop?

You may also want to run Etrecheck and post its report here.

At the moment I can think of two things to try;

1) Delete Finder preferences:

press command-shift-G, type

~/Library/Preferences and press enter

drag com.apple.Finder.plist to the trash

relaunch the Finder (press command-option-escape select Finder on the list and click Relaunch)

If the above does not fix it you may try

2) Download and run the Combo Update over the present system.

While on the Desktop go to the Finder menu and select Preferences. Under the General pane make sure all checkboxes are checked:

Do what Luis recommended,