Secret Santa random pair allocator
As far as I remember, the game isn't strictly pairs. It's everyone's names in a hat, and everyone gets to draw a random name, redraw if it's your own name. This means you don't need an even number of names.

var pairsUL = document.getElementById('pairs'),
      pairsLI,
      textLI;

newList.forEach(function(currentValue, index){
  pairsLI = document.createElement('li'); // the LI element
  textLI = newList[index].person1 + ' and ' + newList[index].person2; // the text for the LI
  pairsLI.appendChild(document.createTextNode(textLI)); // add text to the LI
  pairsUL.appendChild(pairsLI); // append the LI to the UL
});


DOM manipulation is slow. Instead of appending to a live element on each iteration, use a fragment. It's something like an in-memory, not-in-DOM element-like container. Use document.createDocumentFragment() to create one, and append your lis to it. After the loop, append the fragment to your list.

function getRandomInteger(min, max) {
  return Math.round(Math.random() * (max - min)) + min;
}


Instead of Math.round, use Math.floor or append | 0 to the operation. Arrays are zero-indexed. Math.random values range from 0 to 1, excluding 1 itself. This means you'll never get length * 1 and floor will always round down down to the integer before length * 1, the last index in the array.

Readable code is good enough to explain what it's doing. Comments should not explain what the code already does. Instead, it should explain why it was done in that manner. Additionally, you're overloading the lines with long comments. Put them before the code described and limit them to something like 80 characters or 120 characters per line.