White is pretty obvious. He's the white knight.
I think the coolest alias is Mr. Orange. He is an undercover cop. Scenes of his life before the heist are full of blue--the walls in his home, he wears blue jeans and a blue plaid shirt, he practices his backstory on the roof under a clear blue sky. Plus Mr. Blonde refers to the cop in his trunk as "our boy in blue." So the fact that the undercover cop is named Mr. Orange emphasizes that he is playing against his true identity--orange is directly opposite from blue on the traditional color wheel. From cop to crook. From blue to orange. I also don't think it's a coincidence that when Orange is meeting Joe, Eddie, and White in the club, that the club's dance lights are alternating blue and orange behind him.
Mr. Blonde is crazy and doesn't follow the "rules" or the plan everyone had laid out. Similarly, his alias doesn't follow the same pattern as the other guys. They all have traditional color names, and "blonde" while still technically a color doesn't really fit in with the others.
I've been trying to figure Mr. Pink out. The color pink is typically seen as feminine, but I wouldn't say Mr. Pink does anything expressly feminine in the film. Sure, he hides during the Mexican stand-off at the end, but I think that emphasizes more his pragmatism than lack of masculinity. He is first and foremost a practical man, from beginning to end. So perhaps his alias emphasizes his dispassionate, calculated nature. Like bloodless flesh or something. Maybe the only slight feminine reference is the fact that he makes off with the diamonds in the end--Pink with the diamonds, it reminded me of Marilyn Monroe in that pink dress singing, "Diamonds are a Girl's Best Friend." I guess you could argue the lyrics in the song emphasize a similar practicality--diamonds are better than relationships. But that's stretching it, in my opinion.
We don't get enough time with Blue and Brown to draw any real conclusions about their characters. Blue seems pretty calm. Brown, I don't even know.