As long as said user is not a Confluence Administrator then no, they should not be able to see their own group memberships.
Now, you can maybe create a macro which will pull and display a users group membership if thats what you are attempting to accomplish. If this is what are are wanting to do then check out the following:
More and more people are building their careers with Atlassian, and we want you to be at the front of this wave! Important Dates Start the Certification Prep Course by 2 April 2019 Take your e...
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
You're one step closer to meeting fellow Atlassian users at your local meet up. Learn more about AUGs