My experience are just opposite. DATENAME is slower than CONVERT + DATEPART. See below:

/*------------------------

DECLARE @Bitbucket CHAR(4);

PRINT '========== DATENAME Method of Conversion ==========';

SET STATISTICS TIME ON;

SELECT @Bitbucket = DATENAME(yy,SomeDate)

FROM dbo.JBMTest

SET STATISTICS TIME OFF;

PRINT '========== Original Method of Conversion CONVERT ==========';

SET STATISTICS TIME ON;

SELECT @Bitbucket = CONVERT(CHAR(4), DATEPART(yy,SomeDate))

FROM dbo.JBMTest;

SET STATISTICS TIME OFF;

PRINT '========== Original Method of Conversion CAST ==========';

SET STATISTICS TIME ON;

SELECT @Bitbucket = CAST(DATEPART(yy,SomeDate) AS CHAR(4))

FROM dbo.JBMTest;

SET STATISTICS TIME OFF;

------------------------*/

========== DATENAME Method of Conversion ==========

SQL Server Execution Times:

CPU time = 703 ms, elapsed time = 718 ms.

========== Original Method of Conversion CONVERT ==========

SQL Server Execution Times:

CPU time = 562 ms, elapsed time = 578 ms.

========== Original Method of Conversion CAST ==========

SQL Server Execution Times:

CPU time = 579 ms, elapsed time = 579 ms.