Ok so correct me if I'm wrong, but in Dawnguard you gotta kill a couple dragons, correct?

What if you've never gone forward with the main quest of Skyrim (never went to Bleak Falls Barrow) and thus were never named Dragonborn? When you kill the quest-related Dawnguard dragons, wouldn't you absorb their souls? I mean then you can potentially run around with Storm Call but no Fus-Ro-Dah.

Is it possible? Or did they think of this and deal with it somehow?

Good question. I think I may test this. I have been able to collect shouts before I started the main quest (but not unlock them). The dragons were not at the shout location. My guess is that the twin dragons would not be there. You actually do not have to fight them to advance the story.

If you don't do the main quest there is only one dragon you need to kill. But you can't absorb his soul. He calls you Dovahkin, you ask him why, and he says it was just instinct or something to call you that and that in the future it may become clear to both of you.

Thankfully, no, you do not need to do the main quest to do Dawnguard.

Yeah but I asked more because I prefer not feeling forced into the position of being the protagonist or being blessed as Dragonborn. That line of dialog you mentioned, yeah that'd kind of annoy me...

The only thing that annoyed me was that the dragon that tells you this, he asks to summon him from the Soul Carin to Tamriel. So you get stuck with a misc. quest to summon him, which you need dragon souls to unlock the shout for. The dialogue itself I actually kinda liked. It was vague enough to make it questionable whether or not you actually are the Dragonborn. It's just a single line of dialogue if it bothers you though.
As for the misc. quest, exiting the dialogue may prevent it from being in the quest log, but I would need to test that to make sure. Aside from the quest to summon the dragon, nothing forces you to be the Dragonborn in this DLC.

I think I heard somewhere that you can attack the dragon and kill him before he speaks to you. I also think I just left the dialogue and he was happy to let me walk away without giving the misc quest.

Right but he didnt actually call you dovahkiin.. He calls you Qahnoarin which means the vanquisher after u kick his butt. for the same reason you mention..

he will call u dovahkiin though only if u already defeated alduin and he'll mention something about alduin defeat was a big news that even the soul cairn people have heard of it!! makes me feel kinda good like yeah i kicked alduin's @$$ now im here to deal with some undeads