OK... my army is the Ultramarines. My Librarian is Tigerius... they just happen to be Ultramarines dressed in yellow and red! Just kidding a little... my army is Ultramarines for tournament purposes but I closely follow guidelines laid out by GW.

I was a little confused by the Space Marines Codex when I first got it. It seemed that only a couple of armies had access to named characters: Raven Guard, Ultramarines, and Imperial Fists. Did that mean I had to paint my armies only a couple of different ways to have some of the most powerful characters in the game? That seemed to fly in the face of what GW explicitly indicated they wanted people to do: create their own chapters! I was at a loss because I wanted to use the named characters but I definitely wanted to create my own fluff. I found the answers in two places:
First, a GW store employee told me that, as long as a unit was game legal it could be used in a tourney no matter how it was painted. Thus, one could paint their Raven Guard pink and blue as long as they followed all the rules for Raven Guard. One note about this: you cannot paint up an army to explicitly look like, say, Black Templars and then go around claiming they are Imperials Fists... that would be deceptive.
The second place (and far more definitive answer) was found in White Dwarf #308 in an article called "What Does 'Counts As' Mean?" It is a wonderfully well written article and it lays out some rules about "Counts As" It says:
" 'Counts As' Is...
1... an opportunity to make a very thematic addition one of your existing armies or create a theme for an all new army.
2... a way of using existing rules to represent a new army or unit type on the tabletop..
3... a chance to play with a unit or model with rules not normally associated with it.
4... a great way to explore the more esoteric aspects of the rich background of Warhammer and 40K.
'Counts As' Is Not...
1... an opportunity to fool or confuse your opponents deliberately.
2... a way to create new rules for your latest passion.
3... an excuse to use proxy models or chits of paper to represent troops."
Its a great article, troops, and I highly recommend it. The net result for Space Marine players is that if you play a Codex Chapter and want to use a named character they cannot take any variences or use the Chapter Trait system. If you want to use Cassius you have to play with straight up Ultramarine rules. If you want to use Lysannder you have to play straight up Imperial Fists. Also, the way I read it doesn't allow for mixing and matching. You can't have Lysannder AND Shrike in the same armies because one named character requires your army be Imperial Fists and the other Raven Guard.
This came up when I showed up to my first Warhammer 40K tournament: Orkapalooza with a yellow and red Tigerius in hand. The judge said, "So your playing Ultramarine army with no traits?" (Forgive me Todd, if I don't have your exact words right). I said, "Yep. Strait up Ultramarines. I just call them the Faithful." He said, "Okay."
The net result is that, if push comes to shove, my army is truly an Ultramarine army painted yellow and red... I'm so ashamed!
PS If you want to see the ultimate "Counts As" army (the Adeptus Mechanicus army by Dave Taylor featured in White Dwarf #308) you can see pics of it at http://warseer.com/forums/showthread.php?t=11246 ... it is a wonder to behold! I think that link is pretty old because it indicates that Taylor was using the IG Codex to represent the army but by the time it was published in WD it was represented by the Lost and the Damned.
PPS There is also more about Taylor's "Counts As" Warhammer 40K army at http://games.groups.yahoo.com/group/adeptusmechanicus/