Name

Reading behind words and their meanings.

From ShoujoBeat vol1 edition:
Kaname means "hinge" or "door". The kanji for his last name is a combination of the old-fashioned way of writing ku,meaning "nine" and ran meaning "orchid". Therefor, Kuran : "nine orchids".

Contribution made by wonderful Aya ^^ and information from http://spencer.blackmarket.net/dic_word_search.asp
The kanji for Kaname (枢) means "hinge, pivot, door".
The first kanji in Kuran (玖) means "beautiful black jewel, nine".
The second kanji for Kuran (蘭), means "orchid, Holland".

A closer approach

Matsuri Hino already made clear that picking her characters name is an important matter, thusefore we can suppose that Kaname's names were picked for their ring but also for their meaning as the plot becomes clearer not only for us readers but for the many characters involved in Vampire Knight.

The first time I heard about Vampire Knight and acknowledged Kaname's name I thought it sounded a bit femenine, sure thing I was watching Full Metal Panic. Fumoffu! at that time so it was easy to associate a female character with Kaname however beyond the first impression -misunderstood- I don't think I were so far away from the overall idea. Kaname althouhg a genuine man is also a vampire and vampires have always been considerated beautiful creatures.
Of course it depends on the kinda of story and vampire, but generally people tend to associate Vampires with Count Dracula, the overused and always fascinating stereotype or again, those wonderful men from "Interview with a Vampire". Either way you want to see it, vampire such as Kaname have that special glow and presence, and then comes the second aspect on his names, in Kuran the ran mean orchid or nine.
Ran is also a farily used name for female characters but can fit perfectly a man. An example? Fujimiya Ran from Weiß Kreuz manga and series, adopts his younger sister name "Aya", in this case the obvious reference to flowers is understandable and in Kaname's case I really think it fits him awesomely.

Remember the orchid is one of the most beautiful and delicate flowers in the world. It is also used in many great occasions and it's beauty is in general higly rated.
This flower demands special attention and is always taken great care of.
This precious sense out of this flower also explains the special position our pureblood has in the vampire comunity and how people is willing to give just everything to protect and cherish him.

However, an over-protected natura also brings loneliness and Kaname is not imune to it.

As for maybe the most important and revelating meaning of his names, the "Ku" kanji might represent Kaname's position out of the vampire comunity and directly in Vampire Knight plotline.
A hinge is an important element of a door, withouth hinge... a door just couldn't be open. So you first need a pivot to open or close a door and been able to enter a space.
What if Kaname being the schemer he seems to be is in fact truly trying to build that bridge between human and vampires? A bridge connects two sides of a river, a door connects two rooms.
Kaname might also be the key to Yuki's lost past, we know that the latest events surrounding Yuki's possible past or origin are closely related to the Vampire Hunters comunity and following down this same path Vampire hunters are obviously tracking every single step of the Vampire comunity itself.

Is Kaname the link between Vampires, the Vampire Hunters and Yuki?...So far, his name seems to point in that direction.