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);