How to show day name in SQL Server?

I have a query on the SQL server

I want to display as below:

CDATE      | CDAY
2019-04-01 | Monday
2019-04-02 | Tuesday
...        | ......
2019-04-30 | Tuesday

But I found error as below:

Conversion failed when converting date and/or time from character string.

Please if someone can help

DECLARE @V_DATE DATE = GETDATE()

;WITH CTE_DATE AS (
        SELECT  DATEADD(dd,-(DAY(@V_DATE)-1),@V_DATE) CDATE,
        DATENAME(dw, CONVERT(varchar, DATEADD(dd,-(DAY(@V_DATE)-1),@V_DATE))) CDAY
        UNION ALL
        SELECT  DATEADD(dd,1,CDATE),
        DATENAME(dw, CONVERT(varchar, DATEADD(dw,1,CDAY)))
        FROM    CTE_DATE
        WHERE   DATEADD(dd,1,CDATE) <= DATEADD(dd,-(DAY(DATEADD(mm,1,CDATE))),DATEADD(mm,1,CDATE))

    )
    SELECT * FROM CTE_DATE

Your problem is:

DATENAME(dw, DATEADD(dw, 1, CDAY))

I think you intend:

DATENAME(dw, DATEADD(dw, 1, CDATE))

I would write the CTE as:

WITH CTE_DATE AS (
        SELECT  DATEADD(day ,-(DAY(@V_DATE)-1),@V_DATE) as CDATE, 
                DATENAME(dw, DATEADD(day, -(DAY(@V_DATE) - 1), @V_DATE)) as CDAY
        UNION ALL
        SELECT  DATEADD(day, 1, CDATE),
                DATENAME(dw, DATEADD(dw, 1, CDATE))
        FROM    CTE_DATE
        WHERE   DATEADD(day, 1, CDATE) <= DATEADD(day, -(DAY(DATEADD(month, 1, CDATE))), DATEADD(month, 1, CDATE))

    )
    SELECT *
    FROM CTE_DATE;

Here is a db<>fiddle.

You don't describe what you want the code the code to do. It has unnecessary conversions to string and might be needlessly complicated for what you want to do.