There are several scriptures that actually reveal the fact, when we who have received the 'new birth' from God, Christ, Himself will give us a new name, no one will know, except ourselves; Revelation 2:17, the other reference is found in Revelation 3:12.
I believe that the song was born out of the hope of receiving a name from God, not only did that name give hope, but the freedom one's spirit longs for, and the hope received only from a loving God who always keeps His promises.
Yes, there are other verses, actually there are four verses, which all cry out to Jesus, Please change mah name, whatever the cost, whatever the loss, whatever the gain, just please, 'Change Mah Name'.