todots = (child, valProp = 'name', nestedProp = 'children', result = {}, path = 'root') => {
  if (!child) {
    return
  }
  result[path] = child
  if (child[nestedProp]) {
    for (let c of child[nestedProp]) {
      todots(c, valProp, nestedProp, result, path + '.' + child[valProp])
    }
  }
  return result
}

obj = {
  name: 'child1',
  children: [
    {
      name: 'child of child'
    },
    {
      name: 'child of child',
      children: [
        {
          name: 'child of child'
        }
      ]
    }
  ]
}

console.log(Object.keys(todots(obj, 'name', 'children')))