Definitely. I would strongly advise you to read a number of Poe's short stories which, from start to finish, never once mention the name of the narrator and where the narrator repeatedly refers to himself as "I" without ever giving away his identity. You might try to read the following to see how this works: "The Fall of the House of Usher," "The Black Cat" and "The Tell-Tale Heart." All of these classic stories should give you some idea of how you can write your own fiction without naming the narrator at all, but telling the story from his point of view.
Now, I am not immediately aware of any text that uses "we" throughout the story to indicate a group of unnamed narrators. I supposed "A Rose for Emily" kind of fits this category, as the narrator is really a group of townspeople, but even then individual characters and responses are indicated. To suggest the different voices in this group of narrators you might have to distinguish the characters by talking about appearance or characteristics rather than giving their name.