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From what I've been able to gather in my research, the name de la Roche, de Roche, Roche, da Rocha, Rocha, originates from the family who owned Castle de Roche, in Pembrokeshire, Wales. There was a Godebert "the Fleming" de Ros who is believed to have either accompanied William the Conqueror to Britain, or it may possibly have been his father who came over with the invasion force. Nevertheless, there is record that by 1130, Godebert was the owner of Castle Roche on a rocky outcrop in Pembrokeshire, Wales, which estate was believed to have been bestowed upon Godebert or his father by William the Conqueror. It is through Godebert de Ros' son, Sir Richard FitzGodebert, that the name de la Roche (eventually becoming de Roche, then Roche) came into existence.
Sir Richard FitzGodebert accompanied "Strongbow", Richard de Clare, 2nd Earl of Pembroke, to Ireland in 1169-1170. The FitzGodebert family became known as FitzGodebert de la Roche, as they were from the (de la) "castle on the rock" (or roch/roche) in Pembrokeshire. FitzGodebert established a fortress in Fermoy which came to be known as Castleroche and eventually Castletowneroche. Sir Richard's descendants assumed the name FitzGodebert de la Roche, eventually de Roche, and finally Roche.
Portuguese Branch:
In the 13th century, during the reign of Sancho III of Portugal (1249–1279), we see for the first time the French version of the name, de la Roche, appear on record in Portugal. Monsignor de la Roche arrived in Portugal on his way to the Holy Land, from possibly Flanders, and assisted in the taking of Silves from the Moors. Afonso III of Portugal granted this gentlemen lands in Torres Novas and other locales, as a reward for his services. His descendants used the Portuguese version of this name, da Rocha.
In the 14th century, another wave of Roche family, arrived from Fermoy, County Cork, Ireland where they were Viscounts, and joined with John I of Portugal in his campaign against Castille, to maintain independence of the Portuguese crown (1383-1385 Succession Crisis). This gentleman had three sons: Gomes, Louis, and Raymond. It is from Dom Gomes da Rocha (de Roche) where the Portuguese version of the name continued into later generations.
The Roche name is a name of the Roche. In Fench, it means "dweller of the roche" rocks. Roche live in a rocks.