Very interesting theory ArgusFilch.
I was thinking the other day that the least likely person will be RAB. I was thinking "Who is the least likely person?" Filch, of course! And I definetly think you're right about him having something to prove. He wants to rub it in everyones face that he, a SQUIB, defeated the most powerful wizard of all time. Why else would he leave a name. No one else would really.