Not quite the same.
Likely, they crossed one parent of the hybrid to something else with a trait they wanted. Then they crossed that back to the origional parent, likely more than once, selecting in each generation. Then they would have inbred and selected. Then made testcrosses to see how hybrids of the new parent do.
So the new hybrid might be as little as 1% different from the origional, but the diference should be significant, at least under some conditions. Or it might be as much as 25% different. I can't imagine anything more different than that being given the same name, but I think it would be legal.
Walter

Thank you, Walter. You spelled out in detail what I suspected. I tried bush Early Girls and had poor results compared with the original. I suppose it is legal, the name is copyright and it is spelled out, New, Improved,
Doug

I understand that the Goliath name is more applied by the qualities they are looking for. If you notice the Goliath name is on peppers also. I have grown most of them side by side and there is little or no resemblance in any of them. I like the original, Sunny and Old Fashioned Goliath's. Whether there is any of the same parents or not I don't know. I just no there are very few similarities between them. JME. Jay