House Finale Reference? Same character?

Besides having the same voice / accent the two could in fact be the same character.

In the Pilot, when Chance is recognised: 'yeah aren't you that doctor?' he almost defensively corrects this by saying he's a psychiatrist. He does so with a quick pace with a nervous flash of his eyes.

In House, the main character faked his own death to avoid jail and spend the last months of his best friend's life at his side. After the death of Wilson one can only assume House would become a fugitive, needing to change his name..
(Eldon Chance and Doctor House, are phonetically similar; compare the way both characters introduces himself to new patients)
House was always emotionally vulnerable. Perhaps after time with Wilson and losing Wilson he emotionally matured and became less defensive.
House loves the puzzle, the puzzle of human emotion always fascinated and frustrated him. After Wilson died, he could have gained insight on complex emotion from experience and been drawn to Psychiatry. He could very well be in this particular job (third party referrals) to remain partially detached from patients, but still get his 'puzzles'
Chance is divorced. House always had problems with his romantic relationships, being emotionally closed off. Wilson was dying, even opening up to Wilson could have been a defensive move knowing that was coming.
House loved to teach and correct people. He always struck me as someone having a desire to be a father / teacher. Chance is a father.
House was a rebel without a cause. Chance is an anti hero with a cause.