Cannot delete 'Install macOS Catalina' file on macOS

It is strange it says it's in use when you try to delete it.

With that said, as a last ditch effort open the terminal app, you can find in the LaunchPad or in the Utilities folder in the Applications folder in Finder.

With the terminal open type (don't press anything after typing it)

sudo rm -rf

Then drag the file from the desktop to the terminal window. It should add the file path to the command line after the command above. Hit enter and it should ask for your password. Type it in, (it won't show anything as you type it) and hit enter.

It should then delete the file.

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and and try to delete from there. Reboot normally.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Where are you seeing this file exactly?

If it appears a location in Finder, you may need to eject it before you can delete it.

What are the permissions for it for your user account?

Does it have read and write permissions? You should see your own account under System in the Sharing & Permissions section as shown in your screen shot.