When I set out to write a story, I have a loose idea of what I want that story to look like in my mind. I have a loose idea of what my characters will be like as well. Typically, these are "people" that have already done a great deal of "speaking" to me as I've contemplated the story so that when it comes time to write them, I already feel like I'm talking in the voice of someone I know well. But all writers are different and the writing process is different for every writer. There are writers who won't even sit down to the keyboard until they've worked out most of the major details of their story, or even all of them. There are writers that are more like me, we like to watch our characters grow and change even as we write them. The important thing is that the characters reach the point of being able to exist fully within the page.
When I began writing the series that I'm currently working on wrapping up, The Lonesome Isle, I had a much different storyline in mind for one of my main players, the character of Dominic. He was originally meant to be the "bad guy" in the first book, a static character who was one and done. Through the course of telling his portion of the story, I found that he had much more to say and that he, in fact, became my most dynamic character through the series. Even his counterpart, Elizabeth, who had a lot of growing up to do throughout the series, really didn't go through as many changes as he did. There was another character that started out in The Lonesome Isle that never made it to the finish line. When writing the story, it became clear that this particular character, while he had a place in the beginning of the story, just wasn't cut out to play an important enough role to make it all the way to the end so his character got cut in the process of me working out the details of the story.
Keeping an open mind to character metamorphosis while telling their stories allows them to come to life organically. It also allows you, as the writer, and reader, to manipulate their part in the story until it fits exactly as it should.