She is introduced as member No.14 into Organization XIII. Similar to Roxas, she is one of the few wielders of the Keyblade. Probably since it's a common feature between them, she seems to get along with Roxas well, and opportunities to hang out with both Roxas and Axel increase. Triggered by events during missions, she comes to gradually doubt her own existence.

Xemnas: "Do you desire significance?"

KINGDOM HEARTS

The boy with no memories and no name
appeared in front of the haunted mansion
of the dusk city, Twilight Town.

Xemnas: "You are a new person."

Appearing in front of that boy
was the one called Xemnas, the leader of Organization XIII.
He bestowed the name "Roxas" to the boy.

Roxas: "Again, a dream of that guy."

Then about 1 year later---

KINGDOM HEARTS II

Roxas awakens inside his room in Twilight Town.
For the past few days, he's been having mysterious dreams.

He is spending the remainder of his summer vacation
with his friends. Then mysterious events surrounding
Roxas begin to occur one after another.

Axel: "The wielder chosen by the Keyblade."

Axel, a member of Organization XIII,
appears before Roxas.
He approaches him,
incessantly trying to make Roxas remember something,
but he is unable to remember anything.

Roxas: "Am I feeling Sora...?"

As such things continue,
Roxas comes to have doubt about his own existence.

Roxas: "What will happen to me after this?"

And so Roxas is lead to arrive at the mansion,
where he would come to know the truth about his existence...

Axel: "So... Are you already Marluxia's puppet?"

KINGDOM HEARTS
CHAIN OF MEMORIES

A member of Organization XIII,
Axel is the life of the Organization.
He often goes to Castle Oblivion,
a place controlled by the Organization.

There he comes to meet the Keyblade
wielder Sora and his fellow companions.

Axel: "If Sora disappears,
it could be dangerous for the Organization's plans too."

The plans of Marluxia,
the person in charge of Castle Oblivion,
were thwarted by Sora and company.

Axel alone returns from Castle Oblivion
to the other Organization members,
having harvested some kind of feelings from Sora.

Axel: "The wielder chosen by the Keyblade."

KINGDOM HEARTS II

Axel left Organization XIII to recapture his close friend Roxas,
so he entered into the virtual Twilight Town and
urged Roxas to recall his memories.

Axel: "I'll meet you in the next life."

However, the memories of Roxas won't return,
and in the end Axel has received commands
from the Organization to erase Roxas.