It would have been to painful for her to remember them everyday によって calling them that. I honestly have no idea what they should have called them. I guess the current names are fine. Wait......... Did they mention the names..........?
Well maybe they could have gone with Peeta's moms name for the girl. And Katniss's dads name for the boy. I don't exactly remember または know the names but I think that naming them after parents would be a nice remembrance.
The girl's name should be hope, and the boy's X-avior. They just seem like they are proof that the capitol didnt hav control over katniss any more. That they are there to stay. I'm getting teary eyed :"(