A family member was arrested. How can I prevent his/her name from being published in the local newspapers?

There is nothing you can do. M.G.L. Chapter 41, Section 98F, the public log law, requires local police departments to keep and maintain a daily log, recording in chronological order, all responses to valid complaints received, crimes reported, the names, addresses of persons arrested and the charges against such persons arrested. The local newspapers covering Pembroke have a policy to publish such information without exception. This is necessary because it would not be fair to publish the names of some and not the names of others. 

Exception: Handicapped individuals who are physically or mentally incapacitated to the degree that said person is confined to a wheelchair or is bedridden or requires the use of a device designed to provide said person with mobility, shall be kept in a separate log and shall not be a public record nor shall such entry be disclosed to the public.