Paul - This money making scam has been going on for some time. It caters to those with just the most rudimentary knowledge of the night sky. Most experienced star gazers know that all the stars visible to the naked eye have already had names/designations assigned to them. All the rest are too faint to see without some kind of optical aid.
I assume you did not know this because of your post. As amateurs, we learn by our mistakes and spreading the cautious word on this one is common in the astronomy community.
As Jeff pointed out, it's guaranteed that the star assigned to you (anyone) will not only be impossible to see with the naked eye, it will be very difficult to locate it with standard locating methods, as Jeff tried to do.
A much more "from the heart" gift for your son would be to take him out on a observation session and show him some of the objects (with binos or telescope) that populate our night sky. This would be a nice "one on one" bonding experience that I'm sure he will remember well into his adulthood. If this can't be done due to no equipment or knowledge of where some of these objects are, you can take him to a planetarium show or a local star party put on by a local club.
You can let him pick out a star and draw the stars around it with an arrow pointing to his star with his name, then frame it for his bedroom wall.
There are many ways of "gifting" your son with the night sky with a little imagination with far more appreciation from him than naming a star after him that neither of you may never get to see...and that's so sad And with the above suggestions, it won't cost you any money
And by the way, to the forums!