All contacts that you publish under Publish > Contacts will be shown on the Contacts tab in your public newsroom. When editing a contact, ticking the checkbox that says Show as press contact in the newsroom, will define this contact as a press contact. Which means that the contact will also appear on the main page of your newsroom.
Moreover, stories that you create in your newsroom from now on will by default automatically show your press contacts as related contacts.
If you wish to choose a different contact for a specific story, just pick the contact manually when creating the content in Publish – click on the button Related contacts, and the chosen contact(s) will replace your press contact(s).
When removing or adding press contacts, these will update accordingly on your newsroom in the section Press contacts on your published stories. Except on stories where once a related contact was added manually (see above), as these will keep showing the manually chosen contact(s).