auto-generates month names in any locale

jsbin.nujus.js

var months = [];

for( var i = 0; i < 12; i++ ){
  months.push( new Date(0,i).toLocaleString({},{month:'short'}) );
  // you can also pass a local like : "en-US" instead of an empty object `{}`.
  // an empty object triggers the system's auto-detection
}

console.log(months);

I ran your code and the weirdest thing happened: I got:

January,February,March,March,April,May,June,July,August,September,October,December

Double March???!

Much simpler:

let months = Array.from (Array(12), (v, i) => new Date (0,i).toLocaleString ({},{month:'short'}))

    var monthsfunc = (monthnum) =>
      new Date(2019, monthnum).toLocaleString("default", { month: "long" });

    const monthrange = [...Array(12).keys()].map(monthsfunc);
    console.log(monthrange);

another way but @SkepticaLee had a much easier version :D

//the number 12 is irrelevant
var date = new Date();
var year = date.getFullYear();
var months = [];
var month = 0;
do {
    months.push(new Date(year,month).toLocaleString('default',{month:'long'}));
    month = new Date(year,month+1).getMonth();
} while (month > 0)
console.log(months);