individual contribution no publicity
You can make your own custom field on Contribution records: for example a radio button anonymous donation: yes/no

Then when you generate CivCRM reports you can decide to exclude contact who say yes or say no for any given contribution by using Filters.

If you use Drupal/Views you can pull that data into a page view and with Views PHP module you can rewrite the Names if radio = yes to 'Anonymous'.

Legislation in your country will determine whether or not your org must have the real donor's name in your CRM.