naminéNaminé, first and foremost, is Kairi's Nobody. As such, they are inevitably connected - without her, Kairi is not truly whole. Nobodies are created when a person loses their heart, either to darkness or through Heartless; the empty vessel left behind becomes a Nobody. That's about where Naminé's connection with "traditional" Nobodies ends. Technically, Naminé shouldn't even exist, as Kairi's heart contains no darkness and the empty vessel never changes to a Nobody, but her birth was under unique circumstances. Whilst in a comatose form, Kairi's heart hid within Sora's, and when Sora released Kairi's heart, Naminé was created. This is why she has power over Sora's memories, and is known as a memory witch, and whilst her powers are linked solely with Sora's memories, this can be quite destructive. Anyone he has met will be affected by her meddling, and, in the case of Kairi, Kairi was effectively removed from existence when Naminé replaced Sora's memory of Kairi with images of herself. Kairi was still alive, absolutely, but the implications of this was nothing positive. Much of her life would have disappeared, her memories ruptured.
Anyway, moving back to Naminé! Naminé is first met in Chain of Memories, even though she was born sometime before it. The Organization were the ones to find her in Castle Oblivion and soon used her to their advantage when Sora entered. Eventually, Naminé's good nature and conscience (not to mention probing by a certain Axel) got the better of her, and she chooses to tell Sora the truth. She gives Sora the choice to fix his memories, which he takes. Between the events of Chain of Memories and II, Naminé began the long process of relinking Sora's memories and eventually succeeds. After this, DiZ requests that Riku disposes of her, but feeling that she doesn't deserve this, Riku takes her to Axel and puts her under his protection. Naminé does not appear again until Kairi is trapped in The World That Never Was, where they escape the cell together.
Presently, Naminé and Kairi have been reunited as one being.
Believe in yourself. Come on, hurry!
Though Naminé's actions corrupt Kairi's existence and memories, the pair do not actually meet until late into Kingdom Hearts II. In the prologue, Naminé expresses her desire to meet her other half, and it is then hinted that she is Kairi's Nobody. There is something of acceptance from Naminé - that she must reunite with Kairi to become whole, as she tries to convince Roxas of the same. Whilst Roxas shows resentment to Sora, Naminé never truly does to Kairi. There's an element of jealousy, briefly, in Chain of Memories, as Naminé feels she is always destined to be alone, but it is not so much directed towards Kairi. She has never hated her other half.
The first time Kairi and Naminé meet face to face is when Kairi is imprisoned by Saix. Naminé opens up a portal and encourages Kairi to come through it, and to believe in herself. Kairi perhaps has an inkling of who she is, inexplicably trusting her and taking the offered hand.
The two girls proceed together and aim to escape The World That Never Was. Whilst fleeing the castle, Saix is alerted to their presence and blocks off their exit. He offers Kairi what she wants most: to see Sora. Kairi declines - even if she does want it, she doesn't want it with him around - and adopts a defensive stance alongside Naminé, despite being unarmed. Whilst Saix is merely bemused by this circumstance, Riku appears and forces him away. After naming the hooded figure as Riku, Naminé disappears for much of the remaining time in the world. Presumably, she has faded into Kairi, though has not yet joined with her. She reappears once again when the path to get back to the islands is blocked, opening another portal home with ease, and shares a conversation with Kairi, Roxas, and Sora, before she finally reunites with Kairi, becoming whole again. During the ending sequence, Kairi is seen greeting Sora, and Naminé is momentarily seen smiling to Roxas, through her other self.
From what is seen of the two of them together, they do get on well. Kairi has no qualms against her nobody, never belittles her, and trusts her entirely. Despite the conflicting personas that Roxas and Sora have, Kairi and Naminé seem to be similar, but have their differences. They seem to share a somewhat sisterly relationship, in a way - like twins, perhaps. And need I mention the forgiveness? They've effected each other's lives so much, but even so, they've accepted it and moved on.
For the future, it's somewhat unclear how their relationship will progress. Unless they are separated there doesn't seem to be that much more necessary ground to cover. I would like to see them interact, however, as they would get on well, and together they are unstoppable.