[{"_id":1,"array":[{"name":"name1","nestedArray":[{"value":"v1"},{"value":"v2"}]},{"name":"name2","nestedArray":[{"value":"v1"},{"value":"v2"}]}]}]

db.collection.aggregate([{$set:{array:{$map:{input:"$array",in:{$mergeObjects:["$$this",{$cond:[{$eq:["$$this.name","name2"]},{nestedArray:{$filter:{input:"$$this.nestedArray",cond:{$eq:["$$this.value","v2"]}}}},{}]}]}}}}}])