Getting search results to display ul for text field being inputted into

I had this question after viewing Ajax php search with multiple text fields generated by php.

So, I tried to think about what everyone has said and based on that I have tried to come up with a solution that doesn't require using ID's. At this stage I don't even want to add complexity by adding data-id values.

To recap, an unknown number of text fields will be generated by a user. Depending on their input, 1 could be echoed out, 3 could be echoed out etc. All of which will be identical and look pretty much like this: (I have put 2 together for this example)

<div class="form-group">
	<input type="text" name="name" autocomplete="off">
	<div class="result"></div>
</div>
<div class="form-group">
	<input type="text" name="name" autocomplete="off">
	<div class="result"></div>
</div>

When results are displayed and a user clicks on a li, that text displays in the text field closest or associated to that text field which is exactly what I want.

The problem I am having though is getting the ul to only display in the text field the person is typing in. What is happening now is that if I type in text field 1, the ul shows for both text fields which is wrong. I am struggling to get this line right.

$(".result").closest("ul").html(data);

Here is the full jQuery: ( I commented out the line that did work to display records, but for both text fields instead of just the one)

$(document).ready(function() {
    $("input").keyup(function() {
        var input = $(this).val();
        $(".loader").show();
        if (input.length > 3) {
            $.ajax({
                type: 'POST',
                url: 'insert-ajax.php',
                data: {
                    name: input
                },
                success: function(data) {

                    if (!data.error) {
//                        	$(".result").html(data);
                        $(".result").closest("ul").html(data);
                        $(".loader").hide();
                    }
                }

            });
        }

        if (input.length < 1) {
            $(".loader").hide();
            $(".result").html("");
        }
    });

    $(".result").on("click", "li", function() {
        console.log($(this).text());
        $(this).closest(".result").siblings("input").val($(this).text());
    });

});