Hello Pelle,
I am sorry for the late reply.
There is no settings for not showing the username, but you can tweak the code to remove this. You can put style="display:none;" to the specific file: yourtheme/blog.comment.form.php
<div class="form-row mtm" style="display:none;">
<input class="form-control width-full" type="text" id="esusername" name="esusername" placeholder="<?php echo JText::_('COM_EASYBLOG_USERNAME'); ?>">
</div>
If you don't know how to do this, can you provide us with backend access and ftp access so that we are able to assist you on this issue? Since this is a core file, you must backup this file before you do update Easyblog because this file will be overriden.
Hope this will help.
Thanks.