Anis R.

jQuery(document).ready(function($){

    $("#name").change(function(){
        var name1 = $("textarea#name").val();
        $(this).next('.namme').text("Запам'ятовано");
        createCookie("namme", name1, "1");
    });
    $('.name').trigger('change');



    $('#about').change(function(){
        var about1 = $('#about').val();
        $(this).next('.abbout').text("Запам'ятовано");
        createCookie("abbout", about1, "1");
    });
    $('.about').trigger('change');


});

function createCookie(name, value, days) { 
    var expires; 

    if (days) { 
        var date = new Date(); 
        date.setTime(date.getTime() + (days * 24 * 60 * 60 * 1000)); 
        expires = "; expires=" + date.toGMTString(); 
    } 
    else { 
        expires = ""; 
    } 

    document.cookie = encodeURIComponent(name) + "=" +  
        encodeURIComponent(value) + expires + "; path=/"; 
} 

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div>
        Назва:
        <textarea type="text" class="form-control" class="name" id="name"></textarea>
        <span class="namme"></span>
    </div>

    <div>
        Опис товару:
        <textarea type="text" class="form-control" class='about' id='about'></textarea>
        <span class="abbout"></span>
    </div>