The "best method" depends on how you want to do it.  Assuming you want to do it via T-SQL, then maybe something like below (I've omitted any error/missing object checking):

DECLARE @current_proc_name nvarchar(100);

DECLARE @new_proc_name nvarchar(100);

DECLARE @proc_source nvarchar(max);

SET @current_proc_name = 'proc1';

SET @new_proc_name = 'proc1_new';

SELECT @proc_source = OBJECT_DEFINITION(OBJECT_ID(@current_proc_name));

SET @proc_source = STUFF(@proc_source, CHARINDEX(@current_proc_name, @proc_source), LEN(@current_proc_name), @new_proc_name);

IF CHARINDEX('ALTER', @proc_source) > 0 AND

CHARINDEX('ALTER', @proc_source) < CHARINDEX('SOURCE', @proc_source)

BEGIN

SET @proc_source = STUFF(@proc_source, CHARINDEX('ALTER', @proc_source), 5, 'CREATE')

END /*IF*/

SELECT @proc_source;

EXEC(@proc_source);