Because I couldn't not do it...

getNames.js

function getNames(person) {
  const names = [];
  names.push(person.name);
  person.children.forEach(child => names.push(...getNames(child)));
  return names;
}

const people = {
  name: "Robin",
  children: [
    {
      name: "Alberto",
      children: [
        {
          name: "Quinn",
          children: [
            {
              name: "Conner",
              children: []
            },
            {
              name: "Lila",
              children: []
            }
          ]
        }
      ]
    },
    {
      name: "Charlie",
      children: []
    }
  ]
};

console.log("getNames(people): ", getNames(people));