For custom-delimited date formats, you have to pull out the date (or time) components from a DateTimeFormat object (which is part of the ECMAScript Internationalization API), and then manually create a string with the delimiters you want.

To do this, you can use DateTimeFormat#formatToParts. You could destructure the array, but that is not ideal, as the array output depends on the locale:

{ // example 1
   let formatter = new Intl.DateTimeFormat('en');
   let example = formatter.formatToParts();
   console.log(example);
}
{ // example 2
   let formatter = new Intl.DateTimeFormat('hi');
   let example = formatter.formatToParts();
   console.log(example);
}

Better would be to map a format array to resultant strings:

function join(date, options, separator) {
   function format(option) {
      let formatter = new Intl.DateTimeFormat('en', option);
      return formatter.format(date);
   }
   return options.map(format).join(separator);
}

let options = [{day: 'numeric'}, {month: 'short'}, {year: 'numeric'}];
let joined = join(new Date, options, '-');
console.log(joined);

You can also pull out the parts of a DateTimeFormat one-by-one using DateTimeFormat#format, but note that when using this method, as of March 2020, there is a bug in the ECMAScript implementation when it comes to leading zeros on minutes and seconds (this bug is circumvented by the approach above).

let date = new Date(2010, 7, 5);
let year = new Intl.DateTimeFormat('en', { year: 'numeric' }).format(date);
let month = new Intl.DateTimeFormat('en', { month: 'short' }).format(date);
let day = new Intl.DateTimeFormat('en', { day: '2-digit' }).format(date);
console.log(`{month}-${year}`);

When working with dates and times, it is usually worth using a library (eg. luxon, date-fns, moment.js is not recommended for new projects) because of the many hidden complexities of the field.

Note that the ECMAScript Internationalization API, used in the solutions above is not supported in IE10 (0.03% global browser market share in Feb 2020).

Please do not reinvent the wheel. There are many open-source and COTS solutions that already exist to solve this problem.

Recommended

The following libraries are recommended for new projects.

Luxon (timezones, successor to Moment)

Luxon is the successor to the Moment.js library. It has native time zone and Intl support.

const { DateTime } = luxon;

const value = DateTime
  .fromFormat("2014-08-20 15:30:00", "yyyy-MM-dd HH:mm:ss")
  .toFormat('MM/dd/yyyy h:mm a');

console.log(value); // 08/20/2014 3:30 PM

<script src="https://cdnjs.cloudflare.com/ajax/libs/luxon/3.3.0/luxon.min.js"></script>

js-joda (fixes the Date object)

This is a port of the Joda-Time library in Java. Joda-Time became the java.time package in the Java JDK in version 1.8. It is the successor to the Date object and improves it significantly.

const { DateTimeFormat, DateTimeFormatter, LocalDateTime } = JSJoda;
const { Locale } = JSJodaLocale;

const value = LocalDateTime
  .parse('2014-08-20 15:30:00',
    DateTimeFormatter.ofPattern('yyyy-M-d HH:mm:ss'))
  .format(DateTimeFormatter.ofPattern('MM/dd/yyyy h:mm a')
    .withLocale(Locale.US));
  
console.log(value); // 08/20/2014 3:30 PM

<script src="https://cdn.jsdelivr.net/npm/[email protected]/dist/js-joda.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/@js-joda/[email protected]/dist/index.min.js"></script>

date-fns (fast, tree-shaking, server-side)

This is version 1.x, if you are using Node.js or another server-side JavaScript engine, you should use version 2.x.

const value = dateFns.format(
  dateFns.parse("2014-08-20 15:30:00", "yyyy-MM-dd HH:mm:ss"),
  'MM/DD/YYYY h:mm a');

console.log(value); // 08/20/2014 3:30 pm

<script src="https://cdnjs.cloudflare.com/ajax/libs/date-fns/1.30.1/date_fns.min.js"></script>

Day.js (smallest footprint)

A minimalist date library with plugins.

const value = dayjs("2014-08-20 15:30:00", "yyyy-MM-dd HH:mm:ss")
  .format('MM/DD/YYYY h:mm a');

console.log(value); // 08/20/2014 3:30 pm

<script src="https://cdnjs.cloudflare.com/ajax/libs/dayjs/1.11.7/dayjs.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/dayjs/1.11.7/plugin/customParseFormat.min.js"></script>

date-and-time (small footprint)

A minimalist date library with plugins.

const value = date.format(
  date.parse("2014-08-20 15:30:00", "YYYY-MM-DD HH:mm:ss"),
  'MM/DD/YYYY h:mm A');

console.log(value); // 08/20/2014 3:30 PM

<script src="https://cdn.jsdelivr.net/npm/[email protected]/date-and-time.min.js"></script>

Not recommended

The following libraries are not recommended for new projects, because they are either no longer supported or do not follow best practices.

Moment (timezones, legacy)

Here is the original version using Moment. Since Luxon is the successor to Moment, I have included this as an alternative.

const value = moment('2014-08-20 15:30:00').format('MM/DD/YYYY h:mm a');

console.log(value); // 08/20/2014 3:30 pm

<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.29.4/moment.min.js"></script>

Date.js (small footprint, archived)

This library manipulates the Date prototype. This is not considered best practice.

const value = Date.parse('2014-08-20 15:30:00').toString('MM/dd/yyyy hh:mm tt');

console.log(value); // 08/20/2014 03:30 PM

<script src="https://cdnjs.cloudflare.com/ajax/libs/datejs/1.0/date.min.js"></script>

Without a library

Now, if you really don't want to use a library, a simple tokenizer can assist you in parsing and formatting.

const TOKENS = new Set(['Y', 'M', 'D', 'H', 'h', 'm', 's', 'a']);

const main = () => {
  const value = format(parse('2014-08-20 15:30:00', 'YYYY-MM-DD HH:mm:ss'), 'MM/DD/YYYY h:mm a');
  console.log(value); // 08/20/2014 3:30 pm
};

const parse = (input, pattern) =>
  (tokens => new Date(
    +tokens['Y'] , +tokens['M'] - 1 , +tokens['D'],
    +tokens['H'] , +tokens['m']     , +tokens['s']
  ))(tokenize(input, pattern));

const format = (date, pattern) =>
  pattern.replace(/\b(\w)(\1)*\b/g, (match) => {
    switch (match[0]) {
      case 'Y': return date.getFullYear();
      case 'M': return `${date.getMonth() + 1}`.padStart(match.length, '0');
      case 'D': return `${date.getDate()}`.padStart(match.length, '0');
      case 'h': return `${date.getHours() % 12}`.padStart(match.length, '0');
      case 'm': return `${date.getMinutes()}`.padStart(match.length, '0');
      case 'a': return date.getHours() < 12 ? 'am' : 'pm';
    }
    return capture;
  });

const tokenize = (input, pattern) => 
  pattern.split('').reduce((acc, token, index) => TOKENS.has(token)
    ? { ...acc, [token]: (acc[token] ?? '') + input[index] }
    : acc, {});

main();