If you sign up as a site member, and then tick the option to join the community, your nickname, profile image and social activity on this website will be publicly visible. Making it private takes one simple step which is shown below.
Set to Public/Private
Existing Site Members
Click on the three dots next to your profile picture above, and an option will appear to make your profile private. Click on it and confirm. That's all!
(note: you need to be logged in)
Example
New Site Members
Untick 'join this site's community' when you sign up (see below)