I've literally never heard that or read anything suggesting that. Britain/Britons has been used to describe the islands and peoples of the north Atlantic archipelago since ancient times with great Britain simply referring to the largest island (i.e. England+Scotland+Wales), as per wiki

Written record

The first known written use of the word was an ancient Greek transliteration of the original P-Celtic term. It is believed to have appeared within a periplus written in about 325 BC by the geographer and explorer Pytheas of Massalia, but no copies of this work survive. The earliest existing records of the word are quotations of the periplus by later authors, such as those within Diodorus of Sicily's history (c. 60 BC to 30 BC), Strabo's Geographica (c. 7 BC to AD 19) and Pliny's Natural History (AD 77).[10] According to Strabo, Pytheas referred to Britain as Bretannikē, which is treated a feminine noun.[11][12][13][14] Although technically an adjective (the Britannic or British) it may have been a case of noun ellipsis, a common mechanism in ancient Greek. This term along with other relevant ones, subsequently appeared inter alia in the following works:

Pliny referred to the main island as Britannia, with Britanniae describing the island group.[15][16]
Catullus also used the plural Britanniae in his Carmina.[17][18]
Avienius used insula Albionum in his Ora Maritima.[19]
Orosius used the plural Britanniae to refer to the islands and Britanni to refer to the people thereof.[20]
Diodorus referred to Great Britain as Prettanikē nēsos and its inhabitants as Prettanoi.[21][22]
Ptolemy, in his Almagest, used Brettania and Brettanikai nēsoi to refer to the island group and the terms megale Brettania (Great Britain) and mikra Brettania (little Britain) for the islands of Great Britain and Ireland, respectively.[23] However, in his Geography, he referred to both Alwion (Great Britain) and Iwernia (Ireland) as a nēsos Bretanikē, or British island.[24]

Fuck off British isles is a term used by the occupiers to legitimize their occupation. The Republic is not a part of the British isles