Dirty blonde means you have dark blonde hair. It gets the word "dirty" because common dirt is brown and "dirty blonde" hair is hair that looks as if it is blonde mixed with brown, making the blonde darker. "browny" isn't a word, so you have to think of a synonym for brown, or something that is brown--like dirt. Plus, dirty blonde hair just sounds better than something like "Tree Bark Blonde" don't you think?
Patrisha calls herself "dirty blonde" when, in reality, her hair color is a light brown not a dark blonde color.