Soon after Maxim and the narrator meet, he comments on her Christian name, saying that it is 'lovely and unusual'. She says that the name was given by her father, who was an artist, and that he was 'a lovely and unusual person'. Her father's death, and her being left alone with no assets or income, is the main reason she is now working as a 'paid companion' to the horrible Mrs van Hopper. When he sends a note of apology following their first meeting she comments that her name is on the envelope, and it is spelled correctly, 'something that hardly ever happened', which also marks Maxim as someone who is educated, sensitive, and in tune with her in some way.
So, although we never learn the narrator's first name, we do know that it's 'lovely and unusual' and that Maxim obviously likes and recognises it. Additionally, we can see that her father's contribution to her meeting Maxim de Winter takes a number of forms: he gives her a name which attracts him; his death has led to her presence in his upper class world; and it could also be argued that having had a very close relationship to her father, now dead, she is vulnerable to the offer of another older man to 'look after' her.