This is when a purchaser submits a review.
Even if you enter something like "I wish to remain anonymous" in the name field, your actual name may be reflected.
Are you caching the name from the email address?
I would like the name to appear exactly as it was entered in the name field, is there a setting for that?
If the customer choose "(displayed publicly like Anonymous)", indeed, the review will appear like Anonymous. If the customer want to display the name as it was entered in the name field, they can choose the option "(displayed publicly like John Smith)" so it will display with their full name (or whatever is entered in the name field).
On the merchant side, you can change how the Reviewer name is displayed in this settings: https://judge.me/settings?jump_to=shop+and+reviewer+details.
However, the reviewer's choice would be put in first priority. For example, if the reviewer chooses to display as Anonymous and you have the settings on your store to show the reviewer names as Full name. That specific review would still display as Anonymous instead.
I hope this helps. If you have further concern, please let me know