If you have an official WhatsApp Business Account (Green Badge), Contact Facebook's Direct Support & provide the following details to change display name in your WhatsApp Business Account:
Question Topic: Request an Official Business Account
Request Type: Update OBA Display Name
For a general WhatsApp Business Account, follow the below steps to change your display name:
Go to Business Manager and select your business.
Click "WhatsApp Accounts" & thereon choose WhatsApp Manager.
In WhatsApp Manager, click on "Account Tools".
Now, navigate to the left-most menu and click Phone Numbers.
Under the Name column, hover over your current display name and select the pencil icon.
In the Edit Display Name section, enter a new display name.
Select Next.
That's it!
If your new Display Name is in line with the formatting rules, it will get changed in 2-3 hours!