In the novel Rebecca what was the name of the woman that the narrator worked as a companion to?
It is quite true that her name is never given, which is one du Maurier techniques that focuses attention on the second protagonist and villain of the novel, Rebecca. Since Rebecca is dead when the novel starts, du Maurier employs techniques to bring her to the fore of the reader's mind and equally to make her an ominous and overwhelming character, even though never present. This is one reason why the heroine and first protagonist is never named.
When the book begins, the narrator (we never know her name and we really know very little about her) is working as a companion to a rich American woman named Mrs. Van Hopper. This is how the narrator meets Maxim de Winter -- Mrs. Van Hopper is trying to get to know him because he is an upper-class type and she is trying to get into that level of society.
You might want to look at the way in which the narrator's relationship with Mrs. Van Hopper is paralleled by her relationship with Maxim at the end (or beginning, if you get what I mean) of the story. She seems to play the role of companion for both of them.
The narrator's employer is Mrs Van Hopper. it is interesting to note that she is identified only by her husband's name by marriage, which is all we can deduce about the narrator as well.