Hi,
Please refer below code.
HTML
<div>
<div id="input">
<asp:Label ID="Label1" runat="server" Text=" 06/28/1437"></asp:Label></div>
<h2>
Output Date</h2>
<div id="output">
</div>
<div id="output1">
</div>
<script type="text/javascript">
(function () {
var input = document.getElementById('Label1').innerHTML;
var Date = moment(input, 'MM DD, YYYY');
var eDisplayMoment = document.getElementById('output');
var eDisplayMoment1 = document.getElementById('output1');
var Months = ['Muharram'
, 'Safar'
, 'Rabi\' al-Awwal'
, 'Rabi\' al-Thani'
, 'Jumada al-Ula'
, 'Jumada al-Alkhirah'
, 'Rajab'
, 'Sha’ban'
, 'Ramadhan'
, 'Shawwal'
, 'Thul-Qi’dah'
, 'Thul-Hijjah'
];
eDisplayMoment.innerHTML = Months[parseInt(Date.format('MM')) - 1];
eDisplayMoment1.innerHTML = Date.format('DD');
})();
</script>
</div>
and Change if month names imporper.
Output Date
Jumada al-Alkhirah
28