MongoDb concat string into existiing field

Question

I have the following document:

 {
  "_id":"000001"
  "publicId":"0001"
  "name":John"
 }

Now i would like to concat "M" before each publicId. I did query like this:

db.names.aggregate(
   [
     { $project: { publicId: { $concat: [ "M", "$publicId" ] } }},
      {$out:"names"}
   ]
)

The problem I have is that I lose the name property:

 {
  "_id":"000001"
  "publicId":"M0001"
 }

How can I prevent that?