[{firstArray:[{name:"First object",value:1},{name:"Second object",value:2},{name:"Third object",value:3}],secondArray:[{name:"First object",anotherValue:1},{name:"Second object",anotherValue:2},{name:"Third object",anotherValue:3},]}]

db.collection.aggregate([{$project:{anotherValue:{$map:{input:{$range:[0,{$size:"$firstArray"}]},as:"idx",in:{$mergeObjects:[{$arrayElemAt:["$firstArray","$$idx"]},{$arrayElemAt:["$secondArray","$$idx"]}]}}}}}])