Remove duplicates form an array

With ES6, you could use Set for unique values, after mapping only the names of the objects.

This proposal uses a spread syntax ... for collecting the items in a new array.

const array = [{ id: 123, value: "value1", name:"Name1" }, { id: 124, value: "value2", name: "Name1" }, { id: 125, value: "value3", name: "Name2" }, { id: 126, value: "value4", name: "Name2" }],
      names = [...new Set(array.map(a => a.name))];

console.log(names);

Personally I don't see why everyone is getting all fancy with ES 6. If it were my code I'd prefer to support as many browsers as possible.

var array=[
{id:123, value:"value1", name:"Name1"},
{id:124, value:"value2", name:"Name1"},
{id:125, value:"value3", name:"Name2"},
{id:126, value:"value4", name:"Name2"}
];

   // Create array of unique names
var a = (function(a){
  for (var i = array.length; i--;)
    if (a.indexOf(array[i].name) < 0) a.push(array[i].name);
  return a;
})([]);

console.log(a);

You could also simply combine map with filter

var array = [
  {id:123, value:"value1", name:"Name1"},
  {id:124, value:"value2", name:"Name1"},
  {id:125, value:"value3", name:"Name2"},
  {id:126, value:"value4", name:"Name2"}
];

var unique = array
  .map( item => item.name )
  .filter( ( item, idx, arr ) => arr.indexOf( item ) == idx ) 

console.log(unique)

If you are looking for a JavaScript solution that is not ES 6 (no Set) you can use the Array's reduce method:

var array=[
  {id:123, value:"value1", name:"Name1"},
  {id:124, value:"value2", name:"Name1"},
  {id:125, value:"value3", name:"Name2"},
  {id:126, value:"value4", name:"Name2"}
];
var names = array.reduce(function (a, b) {
  if (a.indexOf(b.name) == -1) {
    a.push(b.name)
  }
  return a;
}, []);

console.log(names);