You cannot fully hide your name in a WhatsApp group
Your group name is shown from your WhatsApp profile name
Change your WhatsApp profile name to a blank or neutral name
Open WhatsApp
Go to Settings
Tap your profile name
Edit the name
Save the new name
If your device allows it, use a blank character as your name
You can also change your profile photo to something neutral
Leave the group if you do not want your name shown there
Ask the group admin to remove your contact name from their phone if they saved it differently