Database

[{name:"parent1",children:{child1:{age:12,isSomething:true},child2:{age:13,isSomething:false},child3:{age:12,isSomething:true}}},{name:"parent2",children:{child4:{age:12,isSomething:true},child5:{age:15,isSomething:false}}}]

Query

db.collection.aggregate([{$set:{obj:{"$objectToArray":"$children"}}},{$set:{obj:{"$filter":{"input":"$obj","cond":{$gte:["$$this.v.age",15]}}}}},{$match:{obj:{$ne:[]}}},{$project:{name:1}}])

Result