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}}}
);