There are people who maintain that they know the answer, and others who say that it is open to conjecture. In the absence of anything from the 'horses mouth' or in black and white or patent law, I suppose it can only be conjecture...
The first extreme hollow grinding originated in Germany, and used a double-wheeled grinding machine. At that time a lot of english blades and steel were sent there to be ground as they had the leading edge technology, so 'Ground in Germany' (or Hamburg) acquired a certain cachet.
Full hollow ground blades make quite a bit of noise in use, and extra hollow ground blades were said to ring or 'sing' - hence the equivalent 'singing blade' for an extra hollow ground razor. Why Hamburg became synonymous with the words 'grind' and 'ring' rather than Solingen - which is about 250 miles away - is a bit obscure, but could be explained by the fact that in the 19th century it was europes third largest port and at the beginning of the 20th century it became a gateway for travel to america and home of the worlds largest transatlantic shipping company. There were certainly a lot of razor makers in Hamburg, but there were more in Solingen. Some say the hollow-grinding machine was made in Hamburg.
Some refer to a 'ring of cities' around Hamburg, which seems a bit like clutching at straws to me and merely an attempt to justify the name by some sort of back derivation.
The technology didn't stay in Germany though - a lot of razors were ground in Sheffield and even english ones that were ground in Germany at some point in their history ended up being ground in Sheffield as Sheffield gained supremacy over Solingen. This gave rise to a few anomalies, like blades with 'Ground in Sheffield' on the tang and "Hamburg Ring' on the blade. Attempts were made to cash-in on the popular term, such as "The Sheffield Ring," "The True Ring," "The Silver Ring," and others.
Giesen & Forsthoff acquired the name as a brand - they are a german company of some pedigree and history, and even they don't know the origin of the term. The real answer is shrouded in the mists of time...
Regards,
Neil