DataTables - Alphabetize names

HTML

<link rel="stylesheet" href="https://cdn.datatables.net/1.10.7/css/jquery.dataTables.css">
<script src="https://cdn.datatables.net/1.10.7/js/jquery.dataTables.min.js"></script>
<h3>jQuery DataTables: Alphabetical search</h3>
<a href="https://www.gyrocode.com/articles/tag/jquery-datatables/">See more articles about jQuery DataTables</a> on <a href="https://www.gyrocode.com/articles/">Gyrocode.com</a><hr>

<table id="example" class="display" cellspacing="0" width="100%">
    <thead>
        <tr>
            <th>Name</th>
            <th>Position</th>
            <th>Office</th>
            <th>Age</th>
            <th>Start date</th>
            <th>Salary</th>
        </tr>
    </thead>
    <tfoot>
        <tr>
            <th>Name</th>
            <th>Position</th>
            <th>Office</th>
            <th>Age</th>
            <th>Start date</th>
            <th>Salary</th>
        </tr>
    </tfoot>
    <tbody>
        <tr>
            <td>Tiger Nixon</td>
            <td>System Architect</td>
            <td>Edinburgh</td>
            <td>61</td>
            <td>2011/04/25</td>
            <td>$320,800</td>
        </tr>
        <tr>
            <td>Garrett Winters</td>
            <td>Accountant</td>
            <td>Tokyo</td>
            <td>63</td>
            <td>2011/07/25</td>
            <td>$170,750</td>
        </tr>
        <tr>
            <td>Ashton Cox</td>
            <td>Junior Technical Author</td>
            <td>San Francisco</td>
            <td>66</td>
            <td>2009/01/12</td>
            <td>$86,000</td>
        </tr>
        <tr>
            <td>Bradley Greer</td>
            <td>Software Engineer</td>
            <td>London</td>
            <td>41</td>
            <td>2012/10/13</td>
            <td>$132,000</td>
        </tr>
        <tr>
            <td>Dai Rios</td>
            <td>Personnel Lead</td>
            <td>Edinburgh</td>
            <td>35</td>
            <td>2012/09/26</td>
            <td>$217,500</td>
       ...

CSS

tr.group, tr.group:hover {
    background-color: #ddd !important;
}

JavaScript

$(document).ready(function () {
    var table = $('#example').DataTable({
        "drawCallback": function (settings){
            var api = this.api();
            
            // Zero-based index of the column containing names
            var col_name = 0;
            
            // If ordered by column containing names
            if (api.order()[0][0] === col_name) {
                var rows = api.rows({ page: 'current' }).nodes();
                var group_last = null;

                api.column(col_name, { page: 'current' }).data().each(function (name, index){
                    var group = name.substr(0, 1);

                    if (group_last !== group) {
                        $(rows).eq(index).before(
                            '<tr class="group"><td colspan="6">' + group + '</td></tr>'
                        );

                        group_last = group;
                    }
                });
            }
        }
    });
});