for the 99.99% of it - I am pretty sure the answer is No because it'd violate privacy norms - but in my school reunion whatsApp group - I have nicknamed my school mate contacts pretty badly ( gave those nicknames to those contacts ) . I'd assume they'd not see "how I refer to them" but just wanted to check
You are right absolutely
Contacts in your phonebook can be named differently or nicknamed as you did in WhatsApp. These nicknames are not shown to your contacts
As far as your group contacts are concerned, they will see your name as they saved in their phonebook / or nicknamed. If they did not save​ your number, the profile name which you added for yourself on your profile photo, is displayed to them as clarified in WhatsApp FAQ
This name will only appear for contacts who do not already have your contact info saved in their phone's address book.
So your WhatsApp nicknames are safe from exposure
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