G.W. Hawthorne notes that ‘expressions such as “your names are written in heaven” (Lk. 10:20), “whose names are in the book of life” (Phil. 4:3), “whose name has not been written … in the book of life” (Rev. 13:8), and “I will not blot his name out of the book of life” (Rev. 3:5), crop up several times within the NT. The figure is taken from the OT (cf. Isa. 4:3; Ezk. 13:9; Dan. 12:1), or from the secular world where a criminal’s name was removed from the civic register to take from him all rights of citizenship.’

Hawthorne appears to offer tentative support for a doctrine of conditional immortality when he adds: ‘If one could argue from these statements that all names have been recorded in the book of life, thereby assuring existence for each person, and if one might also argue that for some reason, e.g., wilful disobedience to God’s commands, deliberate refusal to accept Christ as Savior and Lord, etc., one’s name could be removed from this divine register, “blotted out,” then one might argue that that person would cease to exist, for his name would no longer exist.’

ISBE (2nd ed.), art ‘name’