X-Rite is the company and Eye-One is a product range. The actual product you have is likely to be called the Display 2 or Display XT or something like that.
Colour calibration can not just be done at the press of a button and expect it to work. You need to consider the environment and what you are trying to achieve. Is the room lit by fluros? The calibrated monitor will look different to when it's lit by incandescents. Also many screens do not play nicely with calibration and can take a bit of playing around.
Tell us about the software and what settings you were calibrating against. Tell us about the lighting in your room and the exact process you used to calibrate your screen.
i.e.
how long did you let the screen warm up for before calibration?
what colour temperature target did you calibrate too? 6500k? What is the normal CT of the monitor? If they are very different you are asking for trouble.
did you turn the room lights off before calibrating?
do the room lights shine directly on the screen?
Also as for the branding issue if you have an LCD that pretty much going to be a problem that you can't eliminate. It's pretty much non existent on top of the range 12bit monitors but on most 8bit screens you will see this, and to make things worse most of the LCD panels are actually 6bit. You won't eliminate it so easily.