How to create a partitioned table based on date?
As the error message says, any partition-aligned unique index has to include the partitioning key in the index key.  This requirement exists so the engine can enforce uniqueness on updates without checking every partition.

In your case, this means including OrderDate in the nonclustered index key, or having a non-aligned index.  Both are potentially valid choices, depending on your circumstances.  To preserve alignment, your table and index definitions would be:

CREATE TABLE dbo.Orders
(
    OrderID     integer NOT NULL,
    Name        nvarchar(20) NULL,
    OrderDate   date NOT NULL,

    CONSTRAINT PK__Orders_OrderID_OrderDate
        PRIMARY KEY NONCLUSTERED 
            (OrderID, OrderDate)
        ON PS (OrderDate)
)
ON PS (OrderDate);
GO
CREATE CLUSTERED INDEX CX__Orders_OrderDate
ON dbo.Orders (OrderDate)
ON PS (OrderDate);


Of course this changes the uniqueness that the nonclustered index enforces.  Now, only the combination of OrderID and OrderDate is guaranteed to be unique.  It is theoretically possible to add duplicate OrderIDs, so long as the OrderDate is different.  Whether this change of semantic is acceptable to you depends on your circumstances, but it is something to be aware of.

The alternative is to have the nonclustered primary key non-aligned:

CREATE TABLE dbo.Orders
(
    OrderID     integer NOT NULL,
    Name        nvarchar(20) NULL,
    OrderDate   date NOT NULL,

    CONSTRAINT PK__Orders_OrderID
        PRIMARY KEY NONCLUSTERED 
            (OrderID)
        ON [PRIMARY]
)
ON PS (OrderDate);
GO
CREATE CLUSTERED INDEX CX__Orders_OrderDate
ON dbo.Orders (OrderDate)
ON PS (OrderDate);


This preserves the uniqueness of OrderID alone, and has some benefits with queries that compute MIN or MAX aggregates using the index, but you lose the ability to SWITCH partitions in and out without dropping the primary key and recreating it after the switching operation.

You can read more about partitioning in this section of Books Online and more on the issues of aligned and non-aligned indexes in this excellent answer by Remus Rusanu.