We can use case statement as well.

SELECT  DocDate,
    CASE 
        WHEN DAY(DocDate) BETWEEN 1 AND 7 THEN 1
        WHEN DAY(DocDate) BETWEEN 8 AND 14 THEN 2
        WHEN DAY(DocDate) BETWEEN 15 AND 21 THEN 3
        ELSE 4  -- Covers 22nd to end of the month
    END AS Monthpart
FROM mytable;