Anonymity is a concept used at "anonymous" recovery meetings. Christian anonymity is sometimes viewed as being ashamed of one's faith. Don't be a 'secret soldier' we are admonished! A biblical basis for these concerns may be Matthew 10:32-33 (NIV) "Whoever acknowledges me before men, I will also acknowledge him before my Father in heaven. But whoever disowns me before men, I will disown him before my Father in heaven."
But anonymity is not necessarily disowning who you are or your beliefs, it is putting them forward without connection to one's name. This can be for safety, or to present the message apart from the messenger. At times Jesus himself hid for safety, or instructed people not to tell who He was.*
* At this, they picked up stones to stone him, but Jesus hid himself, slipping away from the temple grounds. (John 8:59 NIV)
* Whenever the evil spirits saw him, they fell down before him and cried out, “You are the Son of God.” But he gave them strict orders not to tell who he was. (Mark 3:11-12)
