Not sure what you meant by A <> ''
; but here is an example that should give you the right idea at least.
USE [tempdb] ;
GO
CREATE TABLE [dbo].[tbl]
(
[name] VARCHAR(15) NULL
, [A] VARCHAR(15) NULL
, [B] VARCHAR(15) NULL
, [C] VARCHAR(15) NULL
);
GO
INSERT INTO [dbo].[tbl] VALUES ('name1','A1','','');
INSERT INTO [dbo].[tbl] VALUES ('name2','A2','','C2');
INSERT INTO [dbo].[tbl] VALUES ('name3','','B3','C3');
GO
SELECT
[name]
, [A] AS value1
, CASE WHEN [B] <> '' THEN [B]
WHEN [C] <> '' THEN [C]
ELSE ''
END AS value2
FROM
[dbo].[tbl];
GO
-- Clean up
DROP TABLE [dbo].[tbl];
GO