You can use an IF statement to return a different resultset.

IF @ClassType = 'P' BEGIN
    SELECT
        col
        , col1
        , classType AS English
        , col4
    FROM my_table;
END; ELSE BEGIN
    SELECT
        col
        , col1
        , classType AS Other
        , col4
    FROM my_table;
END;

Or dynamic SQL

DECLARE @Sql nvarchar(max) = 
'SELECT
    col
    , col1
    , classType AS ' + CASE WHEN @ClassType = 'P' THEN 'English' ELSE 'Other' END + '
    , col4
FROM my_table;';

EXEC sp_execute @Sql;

You can use dynamic SQL

DECLARE @classtype CHAR(1);
DECLARE @alias CHAR(10);
DECLARE @sql CHAR(1000);
SET @classtype = 'P';
IF (@classtype = 'P')
BEGIN
    SET @alias = 'English';
END
ELSE
BEGIN
    SET @alias = 'Other';
END
SET @sql = 'select
    col
    , col1
    , classType as ' + @alias +
    ', col4
from my_table';

EXEC (@sql);