The WhatsApp Business display name is your business name that customers see on your WhatsApp Business profile. When you add a new phone number to your WhatsApp Business account in the Meta Business Manager, you assign a display name to it.
The most frequent cause of a display name rejection is that the name is not on your website. WhatsApp says your display name should have a clear link to your Business and should be in line with WhatsApp’s Commerce and Business policies. It should also be consistent with the branding you use on other external sources such as your website.
What does this mean practically?
If your display name is not identical to your Business name, the name needs to be on your website as a program that you run, using exactly the same wording.
If the name is actually the brand name or programme name of a different Business, i.e. if you Google the name and get a different Business’s site, you need to clearly show that you have permission to use the name. You will need the other Business to put your Business's name on their site. And you also need to list that Business on your site. Thereafter you need to log a ticket with both site URLs to Facebook via Business Manager.
Let's explain this using an example:
Let's say your name is Impact.org but the display name for your service needs to be EducateTeens, however if you Google 'EducateTeens' you land on the website business called EducateAll where one of the programmes is called 'EducateTeens'.In this case you need to add 'EducateTeens - on behalf of EducateAll' as a programme on your website. And EducateAll will need to add 'EducateTeens - operated by Impact.org' to their website.
All of this is to show that despite the name belonging to EducateAll, you have permission to use it.