String field value length in mongoDB

For MongoDB 3.6 and newer:

The $expr operator allows the use of aggregation expressions within the query language, thus you can leverage the use of $strLenCP operator to check the length of the string as follows:

db.usercollection.find({ 
    name: { $exists: true },
    $expr: { $gt: [{ $strLenCP: '$name' }, 40] } 
})

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For MongoDB 3.4 and newer:

You can also use the aggregation framework with the $redact pipeline operator that allows you to proccess the logical condition with the $cond operator and uses the special operations $$KEEP to “keep” the document where the logical condition is true or $$PRUNE to “remove” the document where the condition was false.

This operation is similar to having a $project pipeline that selects the fields in the collection and creates a new field that holds the result from the logical condition query and then a subsequent $match, except that $redact uses a single pipeline stage which is more efficient.

As for the logical condition, there are String Aggregation Operators that you can use $strLenCP operator to check the length of the string. If the length is $gt a specified value, then this is a true match and the document is “kept”. Otherwise it is “pruned” and discarded.

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Consider running the following aggregate operation which demonstrates the above concept:

db.usercollection.aggregate([
    { $match: { name: { $exists: true } } },
    { $redact: {
         $cond: [
            { $gt: [ { $strLenCP: "$name" }, 40] },
            "$$KEEP",
            "$$PRUNE"
        ]
    } },
    { $limit: 2 }
])

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If using $where, try your query without the enclosing brackets:

db.usercollection.find({ $where: "this.name.length > 40" }).limit(2);

A better query would be to to check for the field’s existence and then check the length:

db.usercollection.find({ name: { $type: 2 }, $where: "this.name.length > 40" }).limit(2); 

or:

db.usercollection.find({ name: { $exists: true }, $where: "this.name.length > 
40" }).limit(2); 

MongoDB evaluates non-$where query operations before $where expressions and non-$where query statements may use an index. A much better performance is to store the length of the string as another field and then you can index or search on it; applying $where will be much slower compared to that. It’s recommended to use JavaScript expressions and the $where operator as a last resort when you can’t structure the data in any other way, or when you are dealing with a
small subset of data.

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A different and faster approach that avoids the use of the $where operator is the $regex operator. Consider the following pattern which searches for

db.usercollection.find({"name": {"$type": 2, "$regex": /^.{41,}$/}}).limit(2); 

Note – From the docs:

If an index exists for the field, then MongoDB matches the regular
expression against the values in the index, which can be faster than a
collection scan. Further optimization can occur if the regular
expression is a “prefix expression”, which means that all potential
matches start with the same string. This allows MongoDB to construct a
“range” from that prefix and only match against those values from the
index that fall within that range.

A regular expression is a “prefix expression” if it starts with a
caret (^) or a left anchor (\A), followed by a string of simple
symbols. For example, the regex /^abc.*/ will be optimized by
matching only against the values from the index that start with abc.

Additionally, while /^a/, /^a.*/, and /^a.*$/ match equivalent
strings, they have different performance characteristics. All of these
expressions use an index if an appropriate index exists; however,
/^a.*/, and /^a.*$/ are slower. /^a/ can stop scanning after
matching the prefix.