You could keep an array of submitted data and sort the array alpabetically. This solution should work:

      let listOfData = [];
      function add() {
        var name = document.getElementById("id-name").value;

        var address = document.getElementById("id-address").value;

        var content = document.getElementById("id-content").innerHTML;
        listOfData.push({
          personName: name,
          personAddress: address
        });

        document.getElementById("id-content").innerHTML = "";

        listOfData.sort((a, b) => a.personName.localeCompare(b.personName));
        for (let person of listOfData) {
          document.getElementById(
            "id-content"
          ).innerHTML += `${person.personName} <br/> ${person.personAddress}<br/> <hr/>`;
        }
      }

You could create an array and sort it

I wrapped in a form to have simpler event handling. Also no need for javascript: label on an inline event handler

const list = []; // you can get this from localStorage if you want to save across reloads
window.addEventListener("DOMContentLoaded", () => {
  const content = document.getElementById("id-content"),
    nameField = document.getElementById("id-name"),
    addressField = document.getElementById("id-address");
  const show = () => {
    list.sort((a, b) => a.name.localeCompare(b.name))
    content.innerHTML = list.map(({ name, address }) => `${name}<br/>${address}`).join("<hr/>");
  };

  document.getElementById("myForm").addEventListener("submit", e => {
    e.preventDefault();
    const name = nameField.value;
    const address = addressField.value;
    list.push({ name, address });
    show();
  });
});

<form id="myForm">
  Name: <input type="text" id="id-name" name="name"><br /> Address: <textarea id="id-address" name="address"></textarea><br />
  <button id="id-send">Send</button>
</form>
<hr>

<div id="id-content"></div>

Use this code it will work

function add() {
  var name = document.getElementById("id-name").value;
  var address = document.getElementById("id-address").value;
  let data = document.getElementById("id-content");
  let content = data.innerHTML;

  content = content + name + "<br/>" + address + "<hr>";
  
  let dt = "";
  
  let sortArr = content.split("<hr>").sort().join().split(",");
  
  for (let i = 1; i < sortArr.length; i++) {
    dt += sortArr[i] + "<hr>";
  }

  data.innerHTML = dt;
}