How to update document field with reference field value?

Question

Actually have 2 documents: Histories and Subsidiaries, but I forgot add to Histories the subsidiary name.

Histories Document:

{
    "_id" : ObjectId("59480f91ba4d070b882ff924"),
    "subsidiary" : ObjectId("5947fdf3ba4d070b882ff851"),
    "campaignTitle" : "Prueba Autoredeeem",
    "campaignId" : ObjectId("5948004fba4d070b882ff886"),
}

Subsidiary Document

{
    "_id" : ObjectId("5947fdf3ba4d070b882ff851"),
    "loginId" : 50174,
    "name" : "Sucursal Alpha",
}

Now I need update History Document , add a "subsidiaryName" field with "Subsidiary.name" value from Subsidiary Document

This is my first aproach:

db.getCollection('couponredeemhistories')
   .updateMany({}, {$set: {subsidiaryName: 
                   db.getCollection('subsidiaries')
                   .findOne({"_id": ObjectId('5947fdf3ba4d070b882ff851')}, {_id: 0,name: 1})}})

But, the result gives me an Object inside subsidiaryName, instead flat text.

{
    "_id" : ObjectId("59480f91ba4d070b882ff924"),
    "subsidiary" : ObjectId("5947fdf3ba4d070b882ff851"),
    "campaignDescription" : "",
    "campaignTitle" : "Prueba Autoredeeem",
    "campaignId" : ObjectId("5948004fba4d070b882ff886"),
    "subsidiaryName" : {
        "name" : "Sucursal Alpha"
    }
}

Then, I have 2 problems:

1. How to set only flat text value to subsidiaryName field? R: Add .name to project for get flat text

2. How to set .findOne() "id" param for current document instead ObjectId('HARD CODE')? R: Iterate with forEach Cursor

IMPORTANT LIMITS: this is for MongoDB Shell (MongoDB 3.4)

Thank you, please support me for fix any language issues on this question.

Updated Answers thanks to @Astro:

db.getCollection('couponredeemhistories').find()
.forEach(function(doc){
    if(doc.subsidiary !== undefined){
        doc.subsidiaryName = db.getCollection('subsidiaries').findOne({'_id': doc.subsidiary}, {_id: 0, name: 1}).name;
        db.getCollection('couponredeemhistories').save(doc);
    }
    })

Answer 1

Try this:

db.getCollection('couponredeemhistories')
   .updateMany({}, {$set: {subsidiaryName: 
                   db.getCollection('subsidiaries')
                   .findOne({"_id": ObjectId('5947fdf3ba4d070b882ff851')}, {_id: 0,name: 1}).name}})