@zlm First thing that you need to do is go to Settings->Discussion. Under ‘Other Comments settings’ make the necessary adjustment and click on ‘Save Changes’. There you will have to uncheck this options Comment author must fill out name and e-mail.
Then you could use the custom css option to hide those two fields. In the dashboard, go to Appearance->Theme Options->Design Options Tab->Custom CSS. Paste the following css and click on ‘Save All Changes’.
.comment-form-email, .comment-form-url {
display: none;
}
Hope this helps.
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