MongoDb's $set equivalent in its java Driver

BasicDBObject carrier = new BasicDBObject();
BasicDBObject query = new BasicDBObject();
query.put("YOUR_QUERY_STRING", YOUR_QUERY_VALUE);

BasicDBObject set = new BasicDBObject("$set", carrier);
carrier.put("a", 6);
carrier.put("b", "wx1");        
myColl.updateMany(query, set);

This should work, the answer which is accepted is not right above.

Try something like this:

BasicDBObject set = new BasicDBObject("$set", new BasicDBObject("age", 10));
set.append("$set", new BasicDBObject("name", "Some Name"));
someCollection.update(someSearchQuery, set);

Also look at this example.