All great coaches are thieves.
It would be foolish not to use things others have proven effective.
I wouldn't worry about identity at all- Urban, like all great coaches, has been stealing ideas from others his entire career. He's then molded together everything he has stolen into his own philosophy and adjusted based on his own views. He's taking what he believes is the best of what Oregon does, but that is not at all the same as simply copying.
Also keep in mind that he is playing a recruiting game at every single moment. When he talks about winning, he says we are going to be Alabama. When he talks about offensive speed, he says we will be Oregon. When he talks about defense, he says we will have an SEC defense. Doing so not only sets goals for the current team, but also serves to be public relations- it connects the Bucks to the perceived greatest in each area. This has an affect on how recruits think about Ohio State.