Thanks for reaching back out to the QuickBooks Community. I can see how your business can benefit from this feature, but at this time, there isn't a way to add a customer's name to the PDF estimate. However, you can manually save the PDF and then add it to an email yourself.
I'll send feedback to our Product Developers so they can consider this in one of the upcoming releases. You can always check out our QuickBooks Blog to see what's new in the product.
Read more about estimates through this helpful guide.
Let me know if you have any other concerns. I'm only a comment away. Have a splendid day!