Typically the term public means available to all (as opposed to private), but in a CMS context is still open to edits, and since the term publish means to make something available for public distribution, then publish still seems the best word.
I don't think the term publish necessarily means no longer editable, but in some instances such as non digital media publications then it certainly does. So it may depend on your particular scenario as to how the term publish is interpreted - either by admin or content consumers.
If publish really is not suitable, then Make public might be the nearest option if you have an truly open readership.
If you have a limited readership and only want to publish in an enclosed circle, then simply Share, Announce or Distribute may be more appropriate - but it also matters how the notification is broadcast to readers. These last three terms suggest more about access control being retained by the publisher, as opposed to something being open or published where the control is placed more in the hands of the reader.