function solve() {
  const inputField = document.getElementsByTagName('input')[0];
  let list = document.getElementsByTagName('li');

  document
      .getElementsByTagName('button')[0]
      .addEventListener('click', () => {
          let name = inputField.value;
          if (name) {
              let resultName = name[0].toLocaleUpperCase();
              let index = resultName.charCodeAt(0) - 65;
              resultName += name.slice(1).toLowerCase();
              if (list[index].textContent.length <= 0) {
                list[index].textContent += resultName;
            } else {
                list[index].textContent += ', ' + resultName;
            }
              inputField.value = ''
          }
      })
}

Жалко че за този toLowerCase() взима толкова много точки!