There are three people around that age in this thread who admitted to knowing the name, but could not identify with his music and didnt know any of his songs. And two of those people (heels & relaxed) are gigantic music fans.
I would bet nearly EVERY SINGLE FUCKING PERSON ON THIS SITE not only knows who Britney Spears is, but can instantly recognize her music. She is far more recognizable that West, I don't even think it's worth debating, frankly.
I knew his name, and after investigating, recognized some of his songs. And even though I knew the songs, I wouldnt have known most of them were his if they had come on the radio or whatever.
And i'm your perfect test subject to determine how "memorable" or "recognizable" he is, because im not part of his fan base and I dont enjoy his genre of music. If he was so transcendent of his bubble (you know, like a real famous musician like Spears), his fame and recognizability (is that a word?) would extend to people like me. White guys over 30 who think his music sucks, and wouldnt be caught dead listening to it. Eminem, Spears, and a host of others succeed in this, West falls short.
I dont care if you think he's more talented, or if he's more critically acclaimed. That doesnt mean anything in terms of the question in the OP.