Query for documents where array size is greater than 1

There's a more efficient way to do this in MongoDB 2.2+ now that you can use numeric array indexes (0 based) in query object keys.

// Find all docs that have at least two name array elements.
db.accommodations.find({'name.1': {$exists: true}})

You can support this query with an index that uses a partial filter expression (requires 3.2+):

// index for at least two name array elements
db.accommodations.createIndex(
    {'name.1': 1},
    {partialFilterExpression: {'name.1': {$exists: true}}}
);

Update:

For mongodb versions 2.2+ more efficient way to do this described by @JohnnyHK in another answer.

1.Using $where

db.accommodations.find( { $where: "this.name.length > 1" } );

But...

Javascript executes more slowly than the native operators listed on this page, but is very flexible. See the server-side processing page for more information.

2.Create extra field NamesArrayLength, update it with names array length and then use in queries:

db.accommodations.find({"NamesArrayLength": {$gt: 1} });

It will be better solution, and will work much faster (you can create index on it).