Have modified your code a bit to get a space separated days. Have a look
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
ALTER PROCEDURE [dbo].[sp_GetAllDays_as_month]
@StartingDate varchar(15),
@EndingDate varchar(15)
AS
BEGIN
SET NOCOUNT ON;
DECLARE @Year AS INT,
@FirstDateOfYear DATETIME,
@LastDateOfYear DATETIME
SELECT @year = 2015
SELECT @FirstDateOfYear = CONVERT(datetime,@StartingDate,103)
SELECT @LastDateOfYear = CONVERT(datetime,@EndingDate,103)
DECLARE @ConcatString VARCHAR(4000)
;WITH cte AS (
SELECT 1 AS DayID, @FirstDateOfYear AS FromDate, DATENAME(dw, @FirstDateOfYear) AS Dayname UNION ALL
SELECT cte.DayID + 1 AS DayID, DATEADD(d, 1 ,cte.FromDate), DATENAME(dw, DATEADD(d, 1 ,cte.FromDate)) AS Dayname
FROM cte
WHERE DATEADD(d,1,cte.FromDate) < @LastDateOfYear)
SELECT @ConcatString = COALESCE(@ConcatString + ' ', '') + cast(DayID as varchar(2))
FROM CTE
OPTION (MaxRecursion 370)
SELECT @ConcatString
END