Hi pandeygolu420...,
Refer below sample.
Database
I have made use of the following table Customers with the schema as follows. CustomerId is an Auto-Increment (Identity) column.

I have already inserted few records in the table.

You can download the database table SQL by clicking the download link below.
Download SQL file
Model
public class Customer
{
    public int CustomerId { get; set; }
    public string Name { get; set; }
}
Controller
public class HomeController : Controller
{
    private DBCtx Context { get; }
    public HomeController(DBCtx _context)
    {
        this.Context = _context;
    }
    public IActionResult Index()
    {
        return View();
    }
    [HttpPost]
    public JsonResult AjaxMethod(string name)
    {
        List<SelectListItem> customers = (from customer in this.Context.Customers.Take(10)
                                            select new SelectListItem
                                            {
                                                Value = (customer.CustomerId).ToString(),
                                                Text = customer.Name
                                            }).ToList();
        return Json(customers);
    }
}
View
@addTagHelper*, Microsoft.AspNetCore.Mvc.TagHelpers
@{
    Layout = null;
}
<!DOCTYPE html>
<html>
<head>
    <meta name="viewport" content="width=device-width" />
    <title>Index</title>
    <style type="text/css">
        body {
            font-family: Arial;
            font-size: 10pt;
        }
    </style>
</head>
<body>
    <form method="post" asp-controller="Home" asp-action="Index">
        <select id="ddlCustomers" multiple="multiple">
            <option value="0">--Select Customer--</option>
        </select>
        <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/select2@4.0.13/dist/css/select2.min.css" />
        <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
        <script type="text/javascript" src="https://cdn.jsdelivr.net/npm/select2@4.0.13/dist/js/select2.min.js">
        </script>
        <script type="text/javascript">
            $(function () {
                $.ajax({
                    type: "POST",
                    url: "/Home/AjaxMethod",
                    data: '{}',
                    success: function (response) {
                        var ddlCustomers = $("#ddlCustomers");
                        ddlCustomers.empty();
                        $.each(response, function () {
                            ddlCustomers.append($("<option></option>").val(this['Value']).html(this['Text']));
                        });
                        $("#ddlCustomers").select2();
                    },
                    failure: function (response) {
                        alert(response.d);
                    },
                    error: function (response) {
                        alert(response.d);
                    }
                });
            });
        </script>
    </form>
</body>
</html>
For more details on multiselect dropdownlist refer