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.
Source "Missing Links Discovered in Assyrian Tablets".
Virtually all encyclopedias and legitimate history books say that the Phoenicians were indeed Canaanites and that both names come from a purple dye that they extracted from a Levantine mollusk called the murex.
What makes you think that this book "Missing Links" is more authoritative than all other history books?
I wouldn't waste any time on that buffon Inyokern. He can't get anything right, even after you tell him. He's been repudiated and found wrong time after time on his same pet issues, but keeps returning like a bad smell from under the porch.
Your time is better spent petting your dog then trying to teach Inyokern anything.