To be fair, the name high fructose corn syrup is not entirely accurate since it leads people to think that there is a lot of fructose is the product. In reality HFCS is 55% fructose and 45% glucose. Thus there is slightly more fructose, however not as much as the name would imply.
That being said, corn sugar is not necessarily more accurate either. This name implies that this sugar is derived directly from corn. In actuality the sugar in corn is modified through a chemical process that yields the fructose-glucose solution in the proportions listed above. Usually if corn sugar was broken down without this chemical modification you would have equal parts fructose and glucose.
The FDA has six months to consider the name change. If it is approved, then it will take 12-18 months for this change to be implemented. If the change is allowed, there will be ample time for parents to add "corn sugar" to their list of ingredients to check.
In the meantime, watch out for all types of sugars in your kids diets. Americans consume way too much sugar as is, and this recent debate only illustrates what an integral part of our diet sugars have become.