To achieve a blue checkmark on WhatsApp, you simply need to submit an application for an Official Business Account on WhatsApp through your WhatsApp Manager.

Go to Phone numbers in your WhatsApp manager and select the number attached to the account you would like to become an Official Business Account.

Then, in Profile under Official Business Account, select Submit request.
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If you are prompted to increase your business limits to become eligible for an Official Business Account, this simply means that you need to increase high-quality traffic on your number.
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If you want to track your traffic and how close you are to being able to submit a request, you can go to Overview in the top left.

When you scroll down on this page, you will see your Business Status on the right-hand side, including a tracker of your Quality Rating. Once you achieve this target, you can submit a request.
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If Meta approves the application, your WhatsApp profile will receive the blue checkmark, and the display name will automatically be shown to contacts, even if they haven't saved your number in their device.