Organization owners can manage the display of member names in an organization.

Each organization member chooses their own profile name in their settings. For more information, see "Personalizing your profile."
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In the top right corner of GitHub Enterprise Server, click your profile photo, then click Your organizations.  
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Next to the organization, click Settings.  
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In the left sidebar, click Member privileges.  
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Under "Admin repository permissions", select or unselect Allow members to see comment author's profile name in private repositories.  
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Click Save.