I totally get where DJ Lippy is coming from.
WhatsApp shows your phone number but as far as names are concerned it is much the same as Mumsnet, up to a point.
You choose your "WhatsApp Profile Name" (the Display Name) - which can be anything you want and you can change it as often as you like (just like Mumsnet).
However, if someone has your phone number in their own "Contacts" with your real name then on WhatsApp they will see the name that they have entered into their own Contacts, not your WhatsApp Profile name.
If you do not have someone's number in your own contacts then what you see is the person's WhatsApp Profile Name preceded by a tilde ~
Example:
~ Mrs Tiggy Winkle: WhatsApp Profile Name as it appears to anyone who does not have "Mrs Tiggy Winkle's" phone number in their own Contacts.
Sarah (Gym): what person A has entered in their own Contacts for that phone number.
Polly's Mum: what person B has entered into their own Contacts for that phone number.
Basingstoke TERF 2: what person C (a TRA infiltrator?) has entered into their own Contacts for that phone number.
Unless you already have the phone numbers of all the other members of a WhatsApp Group advertised on Mumsnet in your own Contacts (highly unlikely) then you do not know who, for example, this really is:
~ Hermione Granger
(or substitute any non-fictional "real sounding" name of your choosing).
Maybe there are people who have that number in their Contacts as:
Sarah JB
Tiffany (was Andrew)
(So many more examples I could choose. Basically, it could be anyone.)
YOUR WHATSAPP PROFILE NAME
If for perfectly normal reasons you have set your WhatsApp Profile Name as your real name and your real name is, for example, "Anne Jones" then everyone in the Group will see ~ Anne Jones and likely assume that that is your real name: so they will have:
a) what they assume is your real name (Anne Jones)
plus
b) definitely your phone number.
How to edit your profile
https://faq.whatsapp.com/859240711908360/
Also check out:
How to change your privacy settings
https://faq.whatsapp.com/3307102709559968/
(There are also workarounds to hide your WhatsApp Profile Name completely but WhatsApp does not tell you how to do that.)
TRUST
There has been a lot of research on this.
People tend to trust other people when they are in the same Chat Group together because this gives a false sense of security. This applies to all sorts of closed or semi-closed groups, online (and in real life too), eg. "hobby groups".
People tend to trust another person even more if they then engage in one-to-one conversations with them because a false sense of "intimacy" is generated. This happens even when there is no "Group" involved, eg. DMs/PMs on any platform.
If you are contacted by someone you only know because they are in the same WhatsApp Group as you, especially if members have not been vetted in some way before being allowed to join, be VERY cautious.
Finally, even if you are confident that everyone in the Group is a fellow "TERF", you cannot guarantee that everyone can be trusted to keep a confidence, whether accidentally or on purpose. There is also absolutely no guarantee that someone will not share screenshots outside the Group.
I hope that all makes sense.
BTW I was late coming to WhatsApp so I RTFM. Most people seem to have been using it much longer than me but skipped that stage and just dived straight in.