how to copy elements from one array to another array in javascript?

To insert text into an HTML element it is better to use textContent instead of innerHTML.

Create an array to push the textContent in each iteration:

function rvalue() {
  var array = [];
  var arrayVariable = ['1', '2', '3', '4', '5']
  arrayLength = arrayVariable.length;

  ptags = document.getElementsByName("values");
  for (i = 0; i < ptags.length; i++) {
    ptags[i].textContent = arrayVariable[Math.floor(Math.random() * arrayLength)];
    array.push(ptags[i].textContent);
  }
  console.log(array);
}

p {
  font-size: 20px;
  color: #000000;
}

<body onload="rvalue()">

  <p name="values"></p>
  <p name="values"></p>
  <p name="values"></p>

</body>

Please Note: Your HTML has no opening div element and font-size has invalid value (2xpx).

It will store value in tempArray by index, you can use Array.push for normal insert in replace of tempArray[index] = arrayVariable[index];

tempArray.push(arrayVariable[index]);

and if you may get duplicate value in array if you use .push method then just use this code to remove duplicate entry

tempArray= tempArray.filter(function(val, i){
  return tempArray.indexOf(val)== i; 
});

function rvalue() {
    var arrayVariable = ['1', '2', '3', '4', '5']
    arrayLength = arrayVariable.length;
    var tempArray = [];

    ptags = document.getElementsByName("values");
    for (i = 0; i < ptags.length; i++) {
        var index =
            Math.floor(Math.random() * arrayLength);
        ptags[i].innerHTML = arrayVariable[index];
        tempArray[index] = arrayVariable[index];

    }
    console.log(tempArray);
}

p {
  font-size: 2xpx;
  color: #000000;
 
}

<body onload="rvalue()">
<p name="values"></p>
</div>
<p name="values"></p>
</div>
<p name="values"></p>
</div>

</div>

Like this

function randomizeParagraphs() {
    var possibleValues = ['1', '2', '3', '4', '5'],
        createdValues = [], // Empty array to store created values.
        pTags = document.getElementsByName("values");

    for (var i = 0; i < pTags.length; i++) {
        var item = possibleValues[Math.floor(Math.random() * possibleValues.length)];
        ptags[i].innerHTML = item;
        createdValues.push(item);
    }

    // Log the created values.
    console.log(createdValues);
}

Hey you can assign get values like this,

function rvalue() {
  var arrayVariable = ['1', '2', '3', '4', '5']
  arrayLength = arrayVariable.length;

  arrRandomGeneratedValue = [];
  ptags = document.getElementsByName("values");
  for (i = 0; i < 5; i++) {
    randomGeneratedValue = arrayVariable[Math.floor(Math.random() * arrayLength)];
    ptags[i].innerHTML = randomGeneratedValue;
    arrRandomGeneratedValue.push(randomGeneratedValue);

  }
 return arrRandomGeneratedValue;
}

rvalue();

well I dunno if I understood but if you want to save the random values use the push method in the new array variable that you want to use as storage.

  function rvalue() {
  var b = [];
 var arrayVariable = ['1', '2', '3', '4', '5']
 arrayLength = arrayVariable.length;

   ptags = document.getElementsByName("values");
   for (i = 0; i < ptags.length; i++) {
   ptags[i].innerHTML = arrayVariable[Math.floor(Math.random() * arrayLength)];
   b.push(ptags[i].innerHTML);  
 }
 }

I hope that is what you were looking for :P regards!