While "Bells for John Whiteside's Daughter" has as its ostensible subject a particular little girl, the death of the child is simply a jumping off point for Ransom, causing him to reflect on how someone can be so young, vital, and engaged, and then be gone in the blink of an eye. He shares this reflection with his readers, who can then reflect on this, too, and appreciate the beauty and joy of any young life and its sad loss.
The reference to bells in the poem is a clue to this intent. The bells are summing the entire community to the funeral of this child, telling us that all will mourn her, not just John Whiteside and the narrator. This may be an allusion to John Donne's famous line, "[T]herefore never send to know for whom the bell tolls; it tolls for thee" (13-14). When any person dies, it is a loss for everyone, since we are all connected and no one person is "an island" (Donne 1).
If Ransom had referred to the child by name in the poem, it would have less of a universal appeal, restricted to one child and her death, rather than a call to all to reflect upon how any child's death diminishes all of us and reminding us of the grace and delight in a young life.