I've looked to see if anyone is talking about this character name and have been unimpressed with the one or two analysis' that flippantly throw out the idea that the Arthur character could be referencing King Arthur of the classic legend.
Sure King Arthur was a leader, as the Inception character Arthur also is in many ways, but where the film Arthur leads in subtly as the point man, the King Arthur leads out of title, strength, and clear authority. Additionally, I just have a hard time finding a connection between these two characters.
Instead, I think the character Arthur pays homage to novelist and scientist Arthur C. Clarke (pictured above).
2001: A Space Odyssey was written by Clarke alongside their writing of the 1968 film by Stanley Kubrick.