If your WhatsApp account is a Business Account, the display name is only shown in the contacts view in smaller text; all other views will show the phone number (unless the account is an Official Business Account).
If your WhatsApp account is an Official Business Account, the display name will be shown in the conversations by default and there will be a green check mark beside the displayed name.
How to request an Official Business Account:
Any Business Account can request to be an Official Business Account. WhatsApp has a process to review Official Business Account requests (to add the verified badge and show name instead of number) by reviewing the business presence on social media and blogs.
Here is the link for documentation.
To ensure a speedy process, you must submit lots of evidence showing your business is well known and official (For example: 3 to 5 articles/websites mentioning your business) to show its notability online. You must also write a paragraph explaining why your business needs to have a WhatsApp Official Business Account (see image below for full submission list).
If your request is rejected, your business must wait another 30 days before submitting again.
How it works:
WhatsApp verifies that an authentic, notable brand owns this account.
WhatsApp approves Official Business Accounts for internationally recognized brands. Being verified on Facebook or Instagram does not help your business become an Official Business Account.
The criteria for WhatsApp Official Business Accounts is based on a number of factors and is different from policies on other platforms. In addition to following WhatsApp's Commerce and Business Policies, businesses need to be:
Notable: Represents a well-known business, often searched brand or entity.
Verified: Has gone through Business Verification and has set up two-step verification.
Most common cause of rejection:
Notability requires a business to represent a well-known, often searched brand or entity. This should not be taken as a signal of the authenticity of the business. A business is considered authentic if they have gone through the Business Verification which verifies the business as a legal entity and their access to the business.
Notability also reflects substantial presence in online news articles. Notability is assessed based on an account’s presence in
news articles from publications with sizable audiences. WhatsApp does not consider paid or promotional content as sources for review, including business or app listings.
Official Business Accounts are issued at the phone number and display name level. WhatsApp assesses notability for the Display Name of the business account that is requesting OBA status. If the display name is changed after receiving the OBA status, WhatsApp will need to reassess the new display name for notability and display name compliance.
Businesses can continue to grow their presence and wait 30 days before submitting another Official Business Account request. It may take time to build the business's presence in news articles as described above.