Who was the mysterious guy with the umbrella

No idea who he was or what he was supposed to represent/symbolize.

I have some questions of my own.

So was the woman - his muse - real at some point or was she just a character in his story? From what I got, she was real at some point in time and she eventually became his muse, but apparently got hit by a car and died. He failed to come to terms with this and this is why he is - in a way - haunted by her. I dunno if that's it or what...

Also does anyone know the name of the credits song? It's pretty good.