Database

db={"country":[{"_id":"5fbc7cc705253c2da4820425","name":"USA"},{"_id":"5fbc7cc705253c2da4820422","name":"PERU"},{"_id":"5fbc7cc705253c2da4820423","name":"COLOMBIA"}],"travel_reservation":[{"name_person":"pablo rojas","countrys_id":[{"country_id":"5fbc7cc705253c2da4820425"},{"country_id":"5fbc7cc705253c2da4820423"}]},{"name_person":"Anuel","countrys_id":[{"country_id":"5fbc7cc705253c2da4820422"}]},{"name_person":"Laura","countrys_id":[]}]}}

Query

db.travel_reservation.aggregate([{$lookup:{from:"country",localField:"countrys_id.country_id",foreignField:"_id",as:"country"}},{$project:{name_person:1,countrys:{$map:{input:"$countrys_id",as:"c",in:{$mergeObjects:["$$c",{name:{$reduce:{input:"$country",initialValue:"",in:{$cond:[{$eq:["$$this._id","$$c.country_id"]},"$$this.name","$$value"]}}}}]}}}}}])

Result