Try with below code:
var month = [];
month[0] = "January";
month[1] = "February";
month[2] = "March";
month[3] = "April";
month[4] = "May";
month[5] = "June";
month[6] = "July";
month[7] = "August";
month[8] = "September";
month[9] = "October";
month[10] = "November";
month[11] = "December";
var d = new Date($("#txtInvMgmtToDate").val());
var monthName = month[d.getMonth()];
alert(monthName);