Each community has a public page that displays the members of the community. A member is displayed on the page if their membership visibility is to public.
A member's visibility is by default set to hidden, and only the member themselves can set their visibility to public to be displayed on the page.
A community manager/owner however can set the membership visibility to hidden of any member in the community.
Go to the Members-tab of your community.
Find the member (or your own membership) in the list of members.
Change the visibility to either hidden or public using the drop-down menu in the Visibility-column. Note that, community owners/managers can only set the visibility to hidden for other members.