Does the customer display name show on any documents/correspondence that is sent to the customer from QuickBooks?

Hi -megabeam-com-au, 

You're correct. The display name you've entered on the customer profile will show on the sales transaction or email you've print or sent to your customer. You may try to check on Print or preview option on an invoice to see how it looks like. 

Also, you can customise the default email message or greetings on your sales forms. Here's how: 

1. Go to Gear icon and select Account and Settings.
2. Select Sales.
3. Select a greeting you prefer.
4. Enter your Email message.
5. You can tick on Email me a copy at (your email address) if you would like to receive a copy of emails you've sent to your customers. 
6. Select Save and Done. 

You can check on this article on how you can add and manage customers in QuickBooks Online.

Feel free to leave a comment below if you have any other questions.