Nah... Accelerator was given to him as his 'Esper Ability' name. But since that guy had no family... or anyone for that matter he kind of got stuck with it as his only identity.
To understand everything... read everything related to 'TOARU Universe'.
Also, as a joke... Accelerator has a genderbent verson of him who is kind of like a kuudure (shy or introvert or whatever... ) character and she is named as 'Yuriko Shuzushina' who has a secret crush on our very own 'Kamijou Touma'. (Well if Accelerator was a female character this is of coure how it would end like)