Database
[{rootName:"AAA",outerItem:{innerItems:[{name:"A"},{name:null},{name:"C"}]}}]
Query
db.collection.update({},[{"$set":{"outerItem.innerItems":{$concatArrays:[{$slice:["$outerItem.innerItems",0,1]},[{$mergeObjects:[{$first:{$slice:["$outerItem.innerItems",1,1]}},{newField:"$rootName"}]}],{$slice:["$outerItem.innerItems",2,{$size:"$outerItem.innerItems"}]}]}}}],{"multi":false,"upsert":false})