I know all of us here on A.net know AS is much more than an Alaskan or West Coast network, but the name 'Alaska' doesn't do them any favors. I think AS should totally rebrand itself.
Yes, people can do research...and WN seems to do all right despite not being limited to 'just' the Southwest...but it takes years, and some of the routes they're trying, unless marketed to the gills, just won't do well because many casual travelers won't think to even check AS for a JFK-SFO routing. They're not trained to do so.
People don't need to do research, the websites do it for them. What percentage of travelers only go to the airline's website? As NameOmitted mentioned, people can go to Orbitz, or any number of other aggregators/GDS fronts and find the cheapest flight, or the flight that'll work for their times, people would fly "Tasmanian Sea Lines" if the price is right. We've seen that borne out with ValuJet, Airtran, Spirit, and Allegiant.
You mentioned WN, which is perhaps where you go the idea of training travelers to check AS for a JFK-SFO routing? Since they don't use the aggregators/GDS for sales to individuals they've had to train the casual traveler to go to their site. Sure AS would like people to go to AlaskaAir.com and buy a ticket directly, but I'm sure they're just fine with people buying through any of the distribution routes.
I have never flown AS, but would love to give them a shot on RDU-SEA. They sound like a great airline. But I think for a lot of East Coast people, they only associate them with AS...don't know they took over VX, have a rather extensive network, etc. Anyway, just looking at it from the casual traveler...we know the difference between an E175 and 739. We know they fly from the Northeast to California, and you don't have to go anywhere near Alaska to use them. I just think a rebrand would do so much for them.
Alaska is Seattle's home airline and is the biggest hub. They literally have half of the airport's departures level, and they have almost half of the market share by passengers. (48.5%, Delta the nearest competitor is 22.2%, Southwest, United, and American all follow with around 6%.) You're kindof saying, "Well, I might fly JetBlue to JFK, but they're an airline I've never heard of before."
Alaska has recently rebranded, and is still repainting the 737s to the new livery. There are several 737s with the older livery flying around. Knowing Alaska, I'm sure they've looked at and studied renaming the airline, but they've come to the conclusion that it isn't worth it. They can still advertise and get their name out, which is the same thing they'd have to do if they renamed, but on a much much larger scale. This isn't like USAir to US Airways where the two names are similar. What name could they go for? AK Airlines? There doesn't seem to be an obvious choice to rename but still call back to the old name.