Yes, three. Diplomatic/Helpful (green and blue), Humorous/Charming (purple, aka Snarky Hawke), and Aggressive/Direct (red). Your first dialogue choice sets your personality, but if you pick enough choices in another vein, it can change. The way to know for sure what personality you have is to select another character, talk to Hawke, and see what she says. It'll be pretty clear which path she's on.

One of the things I found most amusing about my aggro!Hawke in comparison to diplo!Hawke was her reponse to completing the random delivery quests. Diplo!Hawke always said something nice and friendly like "did you lose this?" whereas aggressive!Hawke often said "keep better track of your things!"