Genre is an unidentified sore spot for a lot of writers.
The days of genre defining a writer seem to have passed; a writer who focuses on one field is no longer kept solely to that field when they look for publishers and audiences.
However, this is a limited understanding. Audiences and readers still expect certain things from authors, and authors writing in a genre can still become known for their work in that genre (think George R. R. Martin, who has become known as a fantasy author, or Ursula K. LeGuin, who is known as a science-fiction author).
The stigma on “genre” fiction has mostly fallen away. Pulp is respected as a deliberate writing decision, and the days of being déclassé for deigning to write for a mass audience have ended, at least in the consciousness of readers. High quality upmarket fiction has come out of every major genre, and many of the minor ones. In many cases these books have received major literary awards, and authors who have a “literary” background are moving into the space of speculative fiction in particular. Kazuo Ishiguro, who wrote The Remains of the Day as a profoundly literary work then wrote Never Let Me Go and The Buried Giant as more genre-oriented, but no less profound, works of fiction. Emily St. John Mandel’s Station Eleven blends literary and genre fiction in a way that appeals to literary elites and common readers alike.
So how should you, the writer, define yourself in terms of genre?
Know your work well enough to define it, and know the market well enough to see where you want to take it, but don’t think about writing in a single genre. You can market your fiction with a mass-market or upmarket approach, but all this does is sort your work for a particular community rather than heavily impacting the number of readers, and genres increasingly have upmarket and mass-market overlap.
To lose focus on a particular genre and marketing approach means that you’re going to be looking at different audiences for your work. This does not seem to be the crisis that it once was; readers of fiction by genre and readers of fiction who are primarily loyal to authors have some overlap, and you might pick up some from each camp as you move through different genres.
However, there are difficulties to this approach. You will only succeed if you can put out outstanding pieces in each genre, and if you can reach a target audience. This requires some familiarity with the genre, and a willingness to reach out to the market in a way appropriate to purpose.
When I look at authors who have created significant works across multiple genres and achieved commercial success, I see that they have defined themselves by pointing to an important element in their writing outside the genre. Ishiguro is, essentially, a modern Dostoevsky, giving existential insights to the modern/postmodern existence. LeGuin explores the absolute limits of our understanding and speculates about what could be.
So with that in mind, you can define yourself by genre but it’s not necessarily the best idea.