In this moment with the last version of the C# driver (2.3.0) the only way I found to get the database name specified in connection string is this:
var connectionString = @"mongodb://usr:[email protected],srv2.acme.net,srv3.acme.net/dbName?replicaSet=rset";
var mongoUrl = new MongoUrl(connectionString);
var dbname = mongoUrl.DatabaseName;
var db = new MongoClient(mongoUrl).GetDatabase(dbname);
db.GetCollection<MyType>("myCollectionName");