<div id='time'></div>

var MyDate = new Date,
MyHours = MyDate.getHours(),
elements = document.getElementById('time'),
name = elements.innerHTML;
switch (true){
  case (MyHours >= 5) && (MyHours < 11):elements.innerHTML = 'Доброе утро, ' + name;
  break;
  case (MyHours >= 11) && (MyHours < 16):elements.innerHTML = 'Добрый день, ' + name;
  break;
  case (MyHours >= 16) && (MyHours <= 23):elements.innerHTML = 'Добрый вечер, ' + name;
  break;
  case (MyHours >= 0) && (MyHours < 5):elements.innerHTML = 'Доброй ночи, ' + name;
  break;
  default:elements.innerHTML = 'Здравствуйте, ' + name;
  break;
}