Customer's name doesn't change on the preview, despite changing it in the customer section. I deleted the invoice and made a new one still no change in the name. Why?

You can enter a customer's first and last name on the Customers tab, but there's also the Display name as field that you'll need to check, @warren22. I'll walk you through the steps on how to proceed.

1. Highlight the Sales tab, then select Customers.
2. Locate the customer in question, then click on their name to open the Customers page.
3. Press the Edit button.
4. On the Customer information window, check if you have entered anything in the Display name as field.

At this point, you can either change the text in the Display name as field or use the First name and Last name fields instead. 

On the other hand, if you need to sort the customer list by their last names, see this article for the steps: How to sort the customer list by last name. 

Feel free to post a reply if you have other questions about customer names in QBO. I'll be around to help you out. Enjoy the rest of the day!