She goes unnamed, for a while. Longer than a while. For long, long months, she is 'Sweetie' and she is 'Honey' and she is 'Little one' and she is 'Kid-pissed-on-me' (Haymitch, of course) and she is 'Baby' most of all. Hush-Baby on the nights where she is crying and those cries send both her parents into a panic attack and they are so afraid of touching her, so afraid of hurting her because she is so very frail, and some nights it's only Katniss's mother who tends to her, when the nightmares and the horror are too strong. But she goes unnamed, and she's already six months old and she's still just 'Baby'. They start thinking it just might stay her name.
When she is born, Peeta holds her carefully, big, scarred, calloused hands holding her so, so carefully, with much more ease than Katniss feels she will be able too. He suggests 'Prim' as a kindness, out of love, but all Katniss sees then is her little duck of a sister, the first person she loved, and she sees the fire engulfing her and then the fire is back inside, and she's screaming and screaming until her throat is raw and then Peeta is holding her and somewhere in the big house they are, her mother is taking care of the crying child.
There are hundreds, perhaps even thousands of names to pick, if they want to honor the dead ones (the ones they murdered and failed to protect). Rue. Madge. Wiress. Mags. All those names bring grief and sorrow and they reject them, one after the other. They can't give their daughter something so big to carry. They already carry enough of their ghosts.
They joke about new names. Peeta offers 'Pearl' with a teasing hint of a smile that makes Katniss laugh. Baby is asleep between them and Katniss is still humming her a lullaby over their bed and he says 'Song' and then 'Melody', as he twists her hair between his clever fingers. She smiles, kisses the faded scars on his knuckles, but shakes her head 'no'. They don't carry the same scars the names do, those ones, but it's not something to give a child, either. Not as a name.
Eventually, her mother goes back to her hospital, a kiss to her granddaughter's head, a hug to her daughter and son-in-law. Katniss goes back to hunting without fearing she'll come back and find her husband and daughter dying inside a fire. Peeta takes care of her while he bakes and paints. Baby approaches one year, all blue eyes and smiles and no hunger whatsoever. No fear.
It's springtime, and there are flowers now over the district instead of coal and dust and fire, there is life now and the scent of flowers while she chases after game. She's hunting a deer, her fingers just letting go of the arrow, approaching so she can pick it up when she sees them, and she comes upon her daughter's name.
On her way back, Peeta is playing with their daughter, wiggling his fingers at her. Baby is starting to try and speak, and she makes a sound towards her, small chubby fingers trying to reach her. Peeta seems confused at the flowers she's bringing, knowing what they are for from the family book, more confused when he sees the way she is smiling, the way she's crying as she holds their daughter close.
"Hellow, Yarrow," Katniss says, and that is that.