I have had this question put to me on several occasions, and figured it was about time to put it in writing somewhere I can refer people to, instead of having to tell the tale every convention I go to.
The thing is, they didn't start out as Space Wolves. When I started collecting Warhammer 40K over 20 years ago they didn't have separate codexes, and Space Wolves had a bunker complex, not a Fang (which is way cooler so I'm happy they changed it).
I started doing some painting on models, and after some work and thought stuck on a green and grey colorscheme, with bone shoulderplates and a brown wolf, which I ripped from some other game, but do by hand on each model, so I acctually work for it. I called them Sons of Fenris.
Then 2nd Edition happened. It was a good thing overall, 1st edition had become a mess over the years, with about three different vehicle systems and largely dependent on what White Dwarf articles you had. Collected editions did exist, but some went out of print very fast, or were very expensive. With 2nd edition came the first real codexes.
The Space Wolf codex was acctually a gift. I had read some parts of it, being very annoyed that there homeworld was suddenly a planet called Fenris, forcing me to either rethink my own Chapter, or incorporate this and make them a lost company.
I read the whole codex after I got it, and decided on the later. The character growth from blood claw to long fang and individualism in models simply appealled to me very much, and I've stayed loyal to them since. I did however decide to keep my own colorscheme, disliking the new blue (they used to be grey). It's like painting Dark Angels Green, To my mind they should be black.
There you have it! And here we are 20 odd years later and I'm still adding select models to the force. Because basically Fenris Rules!