How can I set up a user to only see assigned company files on the desktop?

I'll be more than happy to assist you in managing your user permission, @HMN1.

 In QuickBooks Desktop, an individual cannot access a company file if they are not added to it. While you can limit what specific areas of the program they can access, please take note they would still be able to see the other company files when they log into the program.

If you don't want other users to see them, you'll have to place the company file in a folder to which that specific user doesn't have access. You can consult your local IT support when performing this process. I've listed the general steps below:

1. Head to the current location of the company file of QuickBooks Desktop.
2. Right-click on it and select copy.
3. Paste it to another location.
4. Open QBDT and select Open or Restore an Existing Company.
5. Press the Open a Company File option.
6. Find the location of the file where you have pasted it.
7. After you find that, the file is to be highlighted.
8. Hit Open.

You can also visit these articles to learn more about changing and the restrictions of the user roles:

• QuickBooks Desktop users and restrictions
• Create and manage users and roles in QuickBooks Desktop Enterprise

Let me know if you still have questions about user roles. Have a great day, and take care. 

You can limit access to files, but you can't actually hide them using any feature in QuickBooks.

You could put them in a folder that the user has no rights to, I suppose.

I agree, You need to put the company file in a specific folder and you won't share it to everyone.