Visitor Login/Blog Commenting/Anonymous Comments

Site URL: https://www.squarespace.com/

Hi,

I am trying to enable Anonymous Commenting for a Blog on a private site, but users are not getting prompted the "Comment as Guest" pop-up before being able to comment (image below). I am wondering if by using Anonymous Comments, the name of the person is identified next to the comment, or if that information is not visible to visitors.

The goal is for visitors to comment using their unique name/identity, and having that linked to their comment. Currently all users are accessing the site with a single password.  One option could be to use the third party commenting platform, such as Disqus. However, Disqus doesn't seem necessary if I can get Comments to work by either Anonymous Comments or changing my site login permissions so visitors can login with Squarespace accounts in order to comment. 

Please let me know if you have any recommendations.

Thanks!