Spoilers involved! TL;DR at the bottom.
In an interview (1,2,3), the author says the following about the name Narcissa (emphasis mine):
queenmarion: I noticed in the Black Family tree that everyone is named after a constellation. Is this intentional? Does this have any bearing on the plot?
JK Rowling: It's just one of those family traditions, although Narcissa breaks the trend. I had always thought of her as 'Narcissa' so I decided not to change her to match the others when I came up with their names. There's been a lot of speculation that she is in some way linked to Lily and Petunia, because of the flower theme, but I can put that rumour to rest here: she isn't related to them.
While this isn't necessarily true, it does raise a lot of interesting questions about the connection between "Narcissa" and other names of people in the Harry Potter series.
Constellation names in the Black family
For a start, the rest of the Black family are named after constellations:
The fact that Narcissa isn't named after a constellation or star may suggest she is slightly different from the rest of her family, and indeed she is in the fact that, to her, family is more important than Voldemort. But the fact that all their names are part of Greek myths show they are related.
People with flower names
Also mentioned in the quote is the flower theme. Narcissus is a genus of flowering plants which includes the daffodils, and Narcissa is only one of many characters in Harry Potter whose names relate to flowers. This Radio Times article gives a nice list:
Hogwarts itself also plays host to a number of flower-named characters, including Pansy Parkinson, Lavender Brown, Poppy Pomfrey and Beauxbatons visitor Fleur Delacour.
The most important characters with flower names apart from Narcissa are of course the sisters Lily Potter and Petunia Dursley. While JK says that they aren't related to Narcissa, the fact they are all named after flowers might show something else. So what do Lily, Petunia and Narcissa have in common? Well, they all have completely different personalities, but they all have one thing in common. They are all very caring of their sons.
Lily cared for Harry so much she sacrificed herself to save him.
We all know how Harry got that scar. Lily's love for Harry allowed him to be saved, but at the cost of Lily's life.
Petunia may hate Harry, but she is very caring of Dudley.
It is very clear that Dudley is a spoilt child. But this is because Petunia loves him, and is just pampering him too much.
Narcissa cares so much for Draco that she risks her life to protect him.
She is so worried for Draco that she gets Snape to make an Unbreakable Vow to protect him (in Chapter Two of Harry Potter and the Half-Blood Prince).
So we have all three very maternal women linked by their names.
The language of flowers
Similar to the last section, there may be hints in the language of flowers.
There are already signs of this appearing in the books (see here), so the flowers may suggest something about each character.
'Lily' symbolises motherhood, beauty and purity
This site has the following list on what a lily means: royalty and regal bearing, motherhood and fertility, purity and the beauty of youth, passion and drive, renewal and rebirth. Some of these, in particular motherhood, purity and beauty of youth (remember Snape and James both liking her) definitely relate to her character.
Petunia symbolises anger and resentment, in how she acts towards Harry
The same site says that a petunia represents: anger, resentment, being with you is soothing. She is definitely angry and resentful towards Harry for being a wizard. It pretty much sums up her character, except for the maternal side.
What I did find interesting was that further down the page under different colour meanings it says: Pink – Motherly Love, Femininity, Gentleness, Compassion (Although it says this doesn't apply specifically to Petunias.) Motherly love is definitely part of her character, just not so much auntly love.
So there are links for the meaning of each flower to each woman; what about Narcissa?
Well, the same site has quite a range of things that it symbolies, as it veries in different cultures. There were a couple that definitely apply though. It contains Prosperity and wealth, especially in the future and Future misfortune. Both of these are definitely true, the Malfoy family are rich, rich enough for Lucius to buy the entire Slytherin Quidditch team Nimbus 2001s to outdo Harry's 2000.
They certainly aren't a very lucky family. They get in Voldemort's bad books and he gives Draco the task of killing Dumbledore.
This site also has something intersting under the Victorian meanings section:
In the Victorian Language of Flowers Narcissus implies respect, decorum and devotion.
Narcissa is certainly a very devoted mother.
While there isn't quite as much here, there are certainly some links.
But not narcissistic?
The one thing you'd think that the name suggested, it doesn't actually seem to suggest.
There certainly isn't any evidence in the book that Narcissa is Narcissistic. There is some evidence that Bellatrix might be, Lockhart is very Narcissistic, and even Voldemort to some extent is, but there is no evidence for Narcissa. A Narcissist would protect themselves at all costs, but Narcissa risks herself and her relationships in order to protect Draco.
Conclusion and summary
While JK says the name just stuck, there are links to the motherly aspects of Lily and Petunia via flowers, and the fact that she isn't named after a star/constellation shows she might be different from the rest of the Black family in the fact that family is more important than Voldemort to her.
