Hi, @____.

I'm here to help ensure to alphabetized your customer's invoice and payment lists in QuickBooks Desktop. 

I'd like to acknowledge your effort in sharing very detailed information about your concern. I've checked my resources to verify if there's an on-going issue about the customer name list in QuickBooks Desktop, but we have no reports of any. 

I've also replicated this on my QuickBooks sample file, and the name of my customer will show up once I type the first 3 or 4 letters of their name. In this case, let's perform some troubleshooting steps to resolve the issue. You'll need to rebuild and verify the data in QuickBooks Desktop to remove the empty or damaged information from the file. 

Here's how to rebuild the data: 

1. At the top menu bar, click File.
2. Select Utilities, and choose Rebuild Data.
3. Click OK if you receive a prompt to backup your company file. Your computer may display the message QuickBooks is not responding. However, as long as you can see your mouse cursor to move, Rebuild is still ongoing. Wait for it to complete.
4. Click OK when you get the message Rebuild has completed and process the next troubleshooting steps.

To verify the data in QuickBooks, you can follow the detailed steps in this article: Resolve data damage on your company file. 

If the same thing happens, you'll need to re-sort your customer's list by following the steps in this article: Re-sort lists.

This should get you on the right track. Please know that I'm just a post away if you have additional questions about the customer's list. Have a good one.