I went and read through their website. At the very bottom was the following disclaimer:

International Star Registry star naming is not recognized by the scientific community.
Your star’s name is reserved in International Star Registry records only.

Seems a bit pointless then, doesn't it? Registering a Star Name that is recognized by no one - except the ISR.

http://www.starregistry.com/

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Rest enough for the individual man -- too much, and too soon -- and we call it death. But for Man, no rest and no ending. He must go on, conquest beyond conquest. First this little planet with its winds and ways, and then all the laws of mind and matter that restrain him. Then the planets about him and at last out across immensity to the stars. And when he has conquered all the deeps of space and all the mysteries of time, still he will be beginning.