h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

The name for Labrador comes from Portugal. Labrador is the word for "laborer" in that language.

It seems that in the modern age of exploring, Portugal's explorers were among the first to Labrador and nearby Greenland. There was a time where the Pope divided the world along east-west lines, between Spain and Portugal. Portugal got everything east from Brazil to India.

Partly out of a sense of duty, Portugal therefore sent explorers to Greenland and Labrador. Out of a desire for cheap labor, Portugal took anyone they could find (capture) in these places, to work in Portuguese territories. There are stories about how Portugal transplanted some suspiciously blond Greenlanders (descendents of the Norse settlers) to the Azores. But this venture didn't yield a lot of results, which is why Portugal didn't leave an official colony anywhere near there.

This is not to say that Portugal (and Iberia by extension) left no mark in the region. Fishermen from the Basques fished near Labrador regularly throughout the 1500s, and set up some bases there (hence the name "Port-aux-Basques" in Newfoundland). But fishermen from England did that too, in larger numbers. This led to the name "Newfoundland" being assigned to the large island near Labrador.

Newfoundland was not an official English colony for many years; official colonial attempts were made at Baffin Island, North Carolina, and Virginia first. But during the 1600s, England took control of Newfoundland, and therefore a loose control of the nearby Canadian coast which the rival French weren't interested in... which is to say, Labrador. Direct but loose English control of Newfoundland and Labrador continued even after the creation of the Dominion of Canada in 1867; the United Kingdom relinquished its control only after the Second World War.

It would therefore seem, Labrador retained its original Portuguese name due to sheer world disinterest.