How to extract values from a JSON field with Mongodb?
Have you tried with aggregate yet?

Following I used $addField and $project

var c = db.getCollection("json_column")
if (c == null) {
    db.createCollection('json_column');
}
db.getCollection("json_column").remove({});

db.getCollection('json_column').insert({user:{"email": "mail6@mail6.com", "name": "name1"}});
db.getCollection('json_column').insert({user:{"email": "mail2@mail.com"}});
db.getCollection('json_column').insert({user:{"email": "mail7@mail7.com", "name": "mail2"}});
db.getCollection('json_column').insert({user:{"email": "mail3@mail.com"}});
db.getCollection('json_column').insert({user:{"email": "mail5@mail8.com", "name": "name3"}});
db.getCollection('json_column').insert({user:{"email": "mail5@mail9.com", "name": "name4"}});

db.getCollection('json_column').aggregate([
{
    $addFields: {
        "email": "$user.email",
        "name": "$user.name"
    }
},
{
    $project: {
        "user":0
    }
}
]);