In order to do that what I would do if I had not used Moment before is I would look in the docs for the Day of Month section, and I look at the available options. I have the D pattern that prints 1 through 31, Do that prints what we want, 1st, 2nd, 3rd, so on and so forth, and DD that prints the number with a 0 in front of it for the values less than 10.
Now in this case we want to use Do pattern so all we have to do is type it over inside format. I'm going to open up the Terminal and Atom so we can see it refresh in the background, and we're going to type:
console.log(date.format('MMM Do YYYY'));
Saving the file, when it starts, we get March 25th 2018, which is indeed correct:

Now we can also add other characters like a comma:
console.log(date.format('MMM Do, YYYY'));
A comma is not part of the patterns that format expects so it's simply going to pass it through, which means the comma gets shown just as we typed it in March 25th, 2018:

Using format in this way gives us a lot of flexibility as to how we want to print the date. Now format is just one of the many methods. There are a ton of methods on Moment for doing just about anything, although I find I use pretty much the same six in most of my projects. There really isn't a lot of need for most of them although they do exist because they are useful in certain situations.