Both hypothesis are plausible, considering that the Monte Grappa, as also the nearby plateau of Asiago, were under cultural and linguistic teutonic influence.
Therefore we can't say which could be the etymological relation between the Monte Grappa and the Grappa, but we can conferm that with the time Bassano del Grappa, the city at the foot of Monte Grappa, has become deservedly the capital of the most important italian distillat.
Bassano 24 Carati è is obtained distillating the marc of the variaties of the area of DOC Breganze, of which Bassano del Grappa is part of. It is called like this because the Grappa remains for 24 months in oak barrels, that are barrels of capacity of about 200 liters.
The permanence in wood gives the distillate a nice golden colour and soft and fragrant aromas of vanilla, coffee and leaf of tea.