Customization of how your WhatsApp number would appear is multi-faceted, more because WhatsApp uses your phone number mainly for identity creation on the platform. You are not able to change directly how it is going to appear to others, but there are ways around visibility and customization. Let's take a deeper look at what you can do:
Profile Name and Status
While you can't change your number, you can change the profile name and status message to anything you want: Your profile name would be different because every time your contacts get a message from you, it says the profile name. You could change this any amount of times through Settings then Profile, editing the name. Another thing that could tell something about you or tell people something from you is your status message; this is one more personal thing that might make your profile unique.
Privacy settings
WhatsApp has different privacy settings through WhatsApp Number Database which you can decide who can see your phone number and other profile information. In Settings under Privacy, you can decide who can see your last seen, profile photo, about information, status update. In such cases, you might give the permissions to "Everyone," "My Contacts," or "Nobody." That way, this feature will come in handy when you want to customize how your number is perceived and by whom.
Through a Business Account
If you are using WhatsApp for professional purposes, then you can create a WhatsApp Business account. You will be allowed to show a business name instead of just your personal number, and this includes many other additional features such as quick replies and automated messages. It is useful for brands or professionals who want a distinct identity.
Saving Contacts
When giving out your number, there's the method of how you get it saved in the contacts. You might also want to personalize the contact name under which your number gets saved in other people's phones. This will not change how the number is displayed, but can help in creating a certain identity when people receive messages from you.
Using Multiple Numbers
WhatsApp allows one to have multiple accounts on one device with the use of WhatsApp Business or using different numbers. That is pretty handy in case you want to differentiate between personal and professional communications. Every separate account will have a different phone number, which provides the ability to contextualize the interaction with each.
Third-party Applications
Although some of the third-party apps are not endorsed, they may try to help you manage and customize how your WhatsApp appears to other people. In any case, using them poses a risk to your privacy and safety; therefore, every precaution and care should be taken regarding the official features provided by WhatsApp.
Conclusion:
You can't directly change how your WhatsApp number is represented, but there's a way to regulate how it works, using settings and options of profiles and privacy, and even a business account.