JS Bin// source http://jsbin.com/dodukacozo

jsbin.dodukacozo.js

var tags = [
{
id: 3,
name: "Stories",
created_at: "2018-04-06 14:24:25",
updated_at: "2018-04-06 14:24:25",
pivot: {
work_id: 14,
tag_id: 3
}
},
{
id: 5,
name: "Examples",
created_at: "2018-04-06 14:41:35",
updated_at: "2018-04-06 14:41:35",
pivot: {
work_id: 14,
tag_id: 5
}
}
]

var tagArray = []; 

var i, item;
for (i = 0; i < tags.length; i++) {
    for (item in tags[i]) {
        if (item === 'name') {
            console.log(tags[i][item]);
            tagArray.push(tags[i][item]);
        }
    }
}
console.log(tagArray);