How do I remove the self-employed product and delete the "No company name" from my list of QBO companies?

This is not the kind of thing we want you to go through with our support. Don't worry, I know how to solve your problem.

I have a way so the unnecessary QuickBooks account will not be listed in the list. Happy to show the complete process to achieve our task.

I'd suggest creating a dummy user and assigning the unused account to that user. This way, the company will disappear from the Company Selection page. 

Here's how: 

1. Go to the Gear icon and choose Manage users. 
2. Select the Add user button. 
3. Pick an appropriate user type, access rights, and user settings. 
4. Enter the dummy user’s name and email address.
5. Click Save. 

After that, accept the invitation on your own using the dummy email you used. After that, transfer the admin rights to that dummy user. Let me show you how:

1. Open the dummy email and click the Let's go hyperlink to accept the invitation. 

        2. Go back to the Gear icon and select Manage users. 

        3. Click the small drop-down arrow perpendicular to the dummy user and click Make primary admin. 

        4. Check the dummy email and accept the invitation by clicking here in the email. 

        5. Open the account using the dummy user and remove yourself as an admin.

Once done, you're not able to see QuickBooks Online Payments, QuickBooks Online Self Employed and No company name accounts. For more information, see this link: Change the primary admin user in QuickBooks Online.

However, if these accounts are closed, we're unable to take them off your list of accounts. The system will automatically delete it on or after the scheduled date. This way, you can continue to have read-only access to your data for future use.

Moreover, check out the following articles below on how to merge companies and manage company settings:

• Merge companies, data files or copy lists
• Edit company settings in QuickBooks Online

Finally, as Fiat Lux - ASIA mentioned above, to attach images, please click the camera icon. For reference, see the screenshot below:

Should you need additional help in managing your QuickBooks account, you can always find me here. I'm just one comment away.