Rebecca is the narrator's antagonist.
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I think that Rebecca, as the name implies, dominates the novel. The narrator seems to be smothered beneath the weight of Rebecca's presence. While Rebecca is assertive and dominant, the narrator seems passive and not altogether developed as a character. I think the effect here is to show Rebecca as an overpowering force which the narrator is unable and unequipped to take on.
The significance of the narrator remaining unnamed can be found in the fact that throughout most of the novel her character is nothing more than the second Mrs. de Winter. She has no identity of her own, although she will seek to find herself. Timid, self-conscious, and insecure, this poor girl married a man she barely knew and moved into a world she had no knowledge of. If this wasn't bad enough, her arrival at her new home is marked by the presence of another; Rebecca.
Imagine trying to take your place as wife, hostess, and helpmate, only to be daily compared and reminded of the perfection of the one who preceded you in that title. The narrator is understandably overwhelmed, but in her nervousness she makes one mistake after another, giving Mrs. Danvers even more ammunition to undermine her position in the household.
Eventually, Mr. de Winter comes clean about his marriage, his wife, and her death. This eases the situation a bit and allows her to relax. I believe the narrator's name remains untold because there's no need for it. We see her character grow as a person, and infold as an immensely likable heroine; she no longer needs an identity because she has found her own.