Can Name ID block text messages? May 11, 2019 02:03 Follow Unfortunately, Name ID cannot block text messages. Name ID can only block calls or send calls to voicemail. Related articles How do I block Restricted, Private, Unknown, or Anonymous calls? How do I know if I am blocking a number with Name ID? How do I view my history of blocked calls? How do I lookup a number? How do I unblock a number with Name ID?