Regarding this answer, the snapshot function is deprecated in version 3.6, according to this update. So, on version 3.6 and above, it is possible to perform the operation this way:
db.person.find().forEach(
function (elem) {
db.person.update(
{
_id: elem._id
},
{
$set: {
name: elem.firstname + ' ' + elem.lastname
}
}
);
}
);