It is now accepted that Britain has been systematically farmed and settled since the Neolithic Era. The implication is that a network of settlements and system of land organisation was in place by the end of that period, and it follows that any settlements and significant topographical features would most likely have had names applied to them by then. It is not much of a stretch to suspect that at least some of these settlements had names relating to prominent individuals or deities and that some at least were transmitted orally down to later generations.
Emrys George Bowen and Barry Cunliffe both place Cornwall and the Cornish as an ethnographic group firmly at the centre of Neolithic, Bronze Age and Iron Age culture and trade based on archaeological and monumental evidence, and given the strong evidence for this hypothesis no one has hitherto seriously refuted it.
Until recently the origins of the Cornish and other insular Celtic peoples was based on the so-called invasion hypothesis, notably promoted by Dillon & Chadwick in the 1960s, who suggested that the arrival of Bronze Age culture was coincident with an invasion by the Beaker People.
Unfortunately this hypothesis creates more problems than it solves as it requires separate events for the introduction of Celtic-languages by invasion from the East c.2,400 BC to Britain and Ireland (co-incident with the start of the Copper working), and an earlier farming related invasion(s), which would have had to pre-date Celtic-languages around c.5,000 BC. As a result this hypothesis is no longer accepted. Furthermore, it is doubted that there was an ethnographic group of Beaker People, and instead the term Beaker Culture is used to relate to the material culture of beaker-style burials.
Gimbutas, Skomal, & Polomé subsequently have suggested several waves of cultural expansion (The so-called Kurgan Hypothesis), where Indo-European languages spread from the Pontic Steppe c.6,000 BC, ultimately leading to a linguistically Indo-European Britain, supplanting the original post-Ice Age culture and language. These waves of expansion, by implication, were independent of the movement of peoples and thus neither require invasions or settlement to explain them. However, this still leaves the spread of agricultural practices unexplained.
This hypothesis has more recently been modified by Renfrew who proposes an alternative Anatolian Hypothesis, in which Proto-Indo-European emerged alongside farming and spread from Anatolia much earlier (from 9,000 BC onwards). In this model Indo-European languages, and by extension Italo-Celtic and eventually proto-Celtic ‘diffused’ across Europe, with farming being the vehicle for language transmission and vice-versa. The Anatolian Hypothesis goes on to propose that the Atlantic Seaboard was a principal gateway to Britain, with Cornwall and Brittany playing a major role in the transfer of material and non-material culture.
This potentially solves the problem of the co-origin of Neolithic material culture and the Celtic languages and, at least in broad brush, is the hypothesis most favoured at present. This broadly agrees with genetic studies which shows ancient foundations for DNA along the Western Seaboard, of which Cornish people form a part, overlaying the remnants of earlier neolithic DNA.