What is your source for the idea that Phoenician means red haired? My understanding is that Phoenician is the Greek translation of Canaan, which is related to the word for purple, not red. The word Edom is related to red.
It's doubtful the Phoenicians called themselves that name. The word means "red-haired men", so it presumed to be a nickname. Phoenicians were not Canaanites. Different physical body stock altogether, so there would not be any realtion to "purple".
Source "Missing Links Discovered in Assyrian Tablets". Much of the info came from translation of the tablets, including inscriptions from writings of peoples in the region. Evidently the Phoenicians were rather warlike and got themselves written up fairly regularly. I would guess conflicts and killing were worth going to the trouble of carving accounts thereof in stone.