Get month name from two digit month number

You want to pass the month when you create the Moment object:

var formattedMonth = moment('09', 'MM').format('MMMM'); // September

moment(
    '09',           // Desired month
    'MM'            // Tells MomentJs the number is a reference to month
).format('MMMM')    // Formats month as name

While there's nothing wrong with Kevin's answer, it is probably more correct (in terms of efficiency) to obtain the month string without going through a moment object.

var monthNum = 9;   // assuming Jan = 1
var monthName = moment.months(monthNum - 1);      // "September"
var shortName = moment.monthsShort(monthNum - 1); // "Sep"