Database
[{"_id":"1","Name":"Name1","Children":[{"_id":"1","Name":"Name1","Type":"One"},{"_id":"2","Name":"Name2","Type":"One"},{"_id":"5","Name":"Name5","Type":"Two"},]},{"_id":"2","Name":"Name2","Children":[{"_id":"3","Name":"Name3","Type":"One"},{"_id":"4","Name":"Name4","Type":"Two"},]},{"_id":"3","Name":"Name3","Children":[{"_id":"7","Name":"Name7","Type":"Two"},{"_id":"6","Name":"Name6","Type":"Two"},]}]
Query
db.collection.aggregate([{$addFields:{totalChildren:{$reduce:{input:"$Children",initialValue:0,in:{$add:["$$value",1]}}},dupChildren:"$Children"}},{$unwind:"$dupChildren"},{$project:{"dupChildren._id":0,"dupChildren.Name":0}},{$group:{_id:"$_id",Name:{$first:"$Name"},Children:{$first:"$Children"},totalChildren:{$first:"$totalChildren"},dupChildren:{$addToSet:"$dupChildren"}}},{$addFields:{count:{$size:"$dupChildren"}}},{$match:{$expr:{$ne:["$totalChildren","$count"]}}},{$project:{dupChildren:0,count:0,totalChildren:0}}])