Yes, but it relies on an ES5 feature of JavaScript. This means it will not work in IE8 or older.

var result = objArray.map(function(a) {return a.foo;});

On ES6 compatible JS interpreters you can use an arrow function for brevity:

var result = objArray.map(a => a.foo);

Array.prototype.map documentation

You can iterate through the object keys and save the name in the array using push:

example = [{
  name: "someone1",
  city: "somewhere1",
  state: "someplace1"
}, {
  name: "someone2",
  city: "somewhere2",
  state: "someplace2"
}];
var arrNames = [];
//iterate through object keys
Object.keys(example).forEach(function(key) {
  //get the value of name
  var val = example[key]["name"];
  //push the name string in the array
  arrNames.push(val);
});
console.log(arrNames);//prints ["someone1", "someone2"]

After @Felix suggestion(with which I agree) there is no need to use Object.keys:

example = [{
  name: "someone1",
  city: "somewhere1",
  state: "someplace1"
}, {
  name: "someone2",
  city: "somewhere2",
  state: "someplace2"
}];
var arrNames = [];
//iterate through object keys
example.forEach(function(item) {
  //get the value of name
  var val = item.name
  //push the name string in the array
  arrNames.push(val);
});
console.log(arrNames); //prints ["someone1", "someone2"]

References

Object.keys()

Array.prototype.forEach()

Array.prototype.push()

You can use array.prototype.find:

var names = [{name: 'joe', age: 'nine'}, {name: 'tom', age: 'ten'}];
var someFun = (nm) => {        
    var found = names.find(el => el.name === nm);
    return found && found.age || null; 
}
console.log(someFun('tom'));

Try This, You get the result you want.

let newArr = [];
for (var key in myVar[0]) {
    if (myVar[0].hasOwnProperty(key)) {
        newArr.push(myVar[0][key]);
    }
}
console.log('New Array: ',newArr);

Output: [ 'A', 'B', 'C', 'D' ]