You can create different users under the “Users” menu of your WordPress admin panel. These would be your various authors.
You just need to set up new users, and whoever the logged in user is will get credit for writing the post.
If you need to edit existing post authors, the edit post screen does have an author dropdown that includes all the registered users who can author posts. If you do not see that dropdown, click Screen Options at the top right of the page, and click the checkbox that says Author.