Where did the word “nickname” originate from ?

It comes from a Middle English word “ekename” . It became nekename when people would misunderstand when someone said, “an ekename” and became nekename and from there to modern “nickname”.

as Timberwolf says. ‘eke’ meant ‘large’ or ‘extra’, so an ‘ekename’ was an addition to your name, not necessarily longer, but something ‘else’.