What if I want to be a writer but another writer already uses my name?

If you like your name on the cover of your book, then go for it. If you were writing children's books and this other author was insanely famous, then I would probably pick a different pen name. I have a common enough name that anyone in any industry has my name. When I publish my book later this year, it will be my name on the cover of my book. I suggest the same for you.