[{items:[{id:1,name:"a",child:[{id:11,name:"aa"},{id:12,name:"bb"}]},{id:2,name:"b",child:[{id:22,name:"ba"},{id:23,name:"bb"}]}]}]

db.collection.update({},{$set:{"items.$[y].child.$[x].name":"cc"}},{arrayFilters:[{"x.id":11},{"y.id":1}]})