Database

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

Query

db.collection.aggregate([{$project:{"array":{"$concatArrays":[{"$filter":{"input":"$array","as":"array","cond":{"$ne":["$$array.name","name2"]}}},{"$filter":{"input":{"$map":{"input":"$array","as":"array","in":{"name":"$$array.name","nestedArray":{"$filter":{"input":"$$array.nestedArray","as":"nestedArray","cond":{"$eq":["$$nestedArray.value","v2"]}}}}}},"as":"array","cond":{"$eq":["$$array.name","name2"]}}}]}}}])

Result