The name traditionally given to those Anglo-Saxons that settled in what is now Hampshire and Dorset which later formed the basis for the kingdom of Wessex. The traditional tale of the genesis of the West Saxons emanates from the Anglo-Saxon chronicle, which tells us that;

AD 495. This year came two leaders into Britain, Cerdic and Cynric his son, with five ships, at a place that is called Cerdic's-ore. AD 514. This year came the West-Saxons into Britain, with three ships, at the place that is called Cerdic's-ore. AD 519. This year Cerdic and Cynric undertook the government of the West-Saxons; the same year they fought with the Britons at a place now called Charford. From that day have reigned the children of the West-Saxon kings.

In other words what one might call the standard Germanic origin myth, which is generally regarded today as being, well, just that, a myth. What the archeological record suggests is that the territory of what was later known as Wessex was first occupied by the same Jutes that established the kingdom of Kent. There were no Saxons, West or otherwise in Wessex at that time, in fact there was no Wessex at all, but rather two Jutish kingdoms based roughly on the areas of Hampshire and the Isle of Wight.

What there was, was a people known as the Gewissae, who were at that time located in the Thames Valley, in the region of Dorchester-on-Thames. Only under pressure from Mercia where they forced to move south and west. Probably sometime in the seventh century, and under the command of their king Caedwalla, these Gewissae invaded the areas of Hampshire, Dorset, and the Isle of Wight.

Bedein his account of the Gewissae lends some support to this modern theory; he describes Caedwalla as "an exile from his country" and tells us that "came with an army, slew Ethelwalch,and wasted that province with cruel slaughter and devastation". Later "he took also the Isle of Wight...and by merciless slaughter endeavoured to destroy all the inhabitants thereof, and to place in their stead people from his own province".

Which has suggested to some that the Gewissae indulged in some old fashioned ethnic cleansing, to others that they merely removed the Jutish royal family and nobility, leaving the bulk of the population (that is the peasants and the slaves)

What is reasonably certain is that it is only after reestablishing a kingdom centred on Winchester that these Gewissae begin calling themselves the "West Saxons" and the kingdom of Wessex came into being. (Although to what extent the Gewissae were actually "Saxon" at all is a matter of debate.)

Which demonstrates that the Anglo-Saxon Chronicle is as much a political document as a work of history , put togther in the ninth century with the specific purpose of providing the kings of Wessex with a suitable history to assist their claim for dominion over the whole of England.


Footnote

The modern theory (if I can call it that) of the genesis of the West Saxons and their relationsip with the Gewissae is based on the work of Dr. Barbara Yorke whose academic credentials and bibliography can be viewed at http://www.wkac.ac.uk/Departments/history/Yorke.htm

I first stumbled across it at the British Channel 4 website, on some pages devoted to the 'Timeteam' live event for 2001. ('Time team' being a C4 series devoted to archeology, by the way.)
Unfortunately C4 seem to have "lost" these pages for the present (otherwise I'd cite them as a source), but they did originally contain a quote from the historian Robin Bush, who said of her theory that it;

has met with general acceptance (I cannot find any historian or archaeologist that disagrees with her conclusions).