I appreciate the image you've shared, @kaye8. I'll provide a workaround that would achieve your goal.
Since the option to select the first name as the display name on the text message while sending the invoice is currently unavailable, the only option is to adjust the Customer display name in their profile. This way, you will only see their given name when you send the transaction to them. I'll show you how:
However, please be aware of scenarios where clients have similar first names. QuickBooks does not allow duplicate names between customers, vendors, and employees. Thus, you'll want to add an identifier like a last name initial to identify which is who.
Moreover, you can run a Transaction List by Customer report or other customer-related reports that show all their information, transactions, and balances.
You might also want to learn specific ways to personalize your reports to fit your reporting preferences: Customize reports in QuickBooks Online.
Once you've edited the display name, the set name will be reflected in the text message.
Just a heads up, we have removed the screenshot containing your personal information to protect your data, as the Community space is a public forum. Let us know if you have questions about managing invoices and other tasks within the program.