MongoDB {aggregation $match} vs {find} speed

That would have to be:

db.users.find({"name": /.*m.*/})

Or, similar:

db.users.find({"name": /m/})

You're looking for something that contains "m" somewhere (SQL's '%' operator is equivalent to regular expressions' '.*'), not something that has "m" anchored to the beginning of the string.

Note: MongoDB uses regular expressions which are more powerful than "LIKE" in SQL. With regular expressions you can create any pattern that you imagine.

For more information on regular expressions, refer to Regular expressions (MDN).

The best way to do this is in version 4.2+ which allows using of aggregation pipeline in the update document and the updateOne, updateMany or update collection methods. Note that the latter has been deprecated in most if not all languages drivers.

###MongoDB 4.2+

Version 4.2 also introduced the $set pipeline stage operator which is an alias for $addFields. I will use $set here as it maps with what we are trying to achieve.

db.collection.<update method>(
    {},
    [
        {"$set": {"name": { "$concat": ["$firstName", " ", "$lastName"]}}}
    ]
)

Note that square brackets in the second argument to the method which define an aggregation pipeline instead of a plain update document. Using a plain document will not work correctly.

###MongoDB 3.4+

In 3.4+ you can use $addFields and the $out aggregation pipeline operators.

db.collection.aggregate(
    [
        { "$addFields": { 
            "name": { "$concat": [ "$firstName", " ", "$lastName" ] } 
        }},
        { "$out": "collection" }
    ]
)

Note that this does not update your collection but instead replace the existing collection or create a new one. Also for update operations that require "type casting" you will need client side processing, and depending on the operation, you may need to use the find() method instead of the .aggreate() method.

##MongoDB 3.2 and 3.0 The way we do this is by $projecting our documents and use the $concat string aggregation operator to return the concatenated string. we From there, you then iterate the cursor and use the $set update operator to add the new field to your documents using bulk operations for maximum efficiency.

###Aggregation query:

var cursor = db.collection.aggregate([ 
    { "$project":  { 
        "name": { "$concat": [ "$firstName", " ", "$lastName" ] } 
    }}
])

###MongoDB 3.2 or newer

from this, you need to use the bulkWrite method.

var requests = [];
cursor.forEach(document => { 
    requests.push( { 
        'updateOne': {
            'filter': { '_id': document._id },
            'update': { '$set': { 'name': document.name } }
        }
    });
    if (requests.length === 500) {
        //Execute per 500 operations and re-init
        db.collection.bulkWrite(requests);
        requests = [];
    }
});

if(requests.length > 0) {
     db.collection.bulkWrite(requests);
}

###MongoDB 2.6 and 3.0

From this version you need to use the now deprecated Bulk API and its associated methods.

var bulk = db.collection.initializeUnorderedBulkOp();
var count = 0;

cursor.snapshot().forEach(function(document) { 
    bulk.find({ '_id': document._id }).updateOne( {
        '$set': { 'name': document.name }
    });
    count++;
    if(count%500 === 0) {
        // Excecute per 500 operations and re-init
        bulk.execute();
        bulk = db.collection.initializeUnorderedBulkOp();
    }
})

// clean up queues
if(count > 0) {
    bulk.execute();
}

###MongoDB 2.4

cursor["result"].forEach(function(document) {
    db.collection.update(
        { "_id": document._id }, 
        { "$set": { "name": document.name } }
    );
})