In the case of the anonymous function expression, the function is anonymous — literally, it has no name. The variable you're assigning it to has a name, but the function does not. (Update: That was true through ES5. As of ES2015 [aka ES6], often a function created with an anonymous expression gets a true name [but not an automatic identifier], read on...)

Names are useful. Names can be seen in stack traces, call stacks, lists of breakpoints, etc. Names are a Good Thing™.

(You used to have to beware of named function expressions in older versions of IE [IE8 and below], because they mistakenly created two completely separate function objects at two completely different times [more in my blog article Double take]. If you need to support IE8 [!!], it's probably best to stick with anonymous function expressions or function declarations, but avoid named function expressions.)

One key thing about a named function expression is that it creates an in-scope identifier with that name for the function within the functon body:

var x = function example() {

    console.log(typeof example); // function

};

x();

console.log(typeof example);     // undefined

As of ES2015, though, a lot of anonymous function expressions create functions with names, and this was predated by various modern JavaScript engines being quite smart about inferring names from context. In ES2015, your anonymous function expression results in a function with the name boo. However, even with ES2015+ semantics, the automatic identifier is not created:

var obj = {

    x: function() {

       console.log(typeof x);   // undefined

       console.log(obj.x.name); // x

    },

    y: function y() {

       console.log(typeof y);   // function

       console.log(obj.y.name); // y

    }

};

obj.x();

obj.y();

The assignment fo the function's name is done with the SetFunctionName abstract operation used in various operations in the spec.

The short version is basically any time an anonymous function expression appears on the right-hand side of something like an assignment or initialization, like:

var boo = function() { /*...*/ };

(or it could be let or const rather than var), or

var obj = {

    boo: function() { /*...*/ }

};

or

doSomething({

    boo: function() { /*...*/ }

});

(those last two are really the same thing), the resulting function will have a name (boo, in the examples).

There's an important, and intentional, exception: Assigning to a property on an existing object:

obj.boo = function() { /*...*/ }; // <== Does not get a name

This was because of information leak concerns raised when the new feature was going through the process of being added; details in my answer to another question here.