They thought of the name 4 AM because they wrote the song at 4:00 AM and Raine Maida 's father , Anthony Maida has the initials `` AM '' . The song title , `` 4am '' , was said by the band that it had double meaningsâ '' that it was completely written at 4:00 am , and it stands for Raine Maida 's father 's initials , Anthony Maida .