Not all countries are named for the people who settled there, in the way that happened with the Angles, Irish and Scots...if they were, France would be Frankland.
Actually - after a little further thought - I should point out that the word 'Welsh' comes from the Latin word 'Volcae', the name of a Gaulish tribe. Many people believe the Romans pronounced 'v' as 'w', so - given that the 'c' might have been soft as in 'face' rather than hard as in 'cat' - one can easily see the source of the sound 'Welsh'.
In the end, therefore, perhaps the country did get its name from the people who settled there!