How to derive new columns in YYYYMM format between two dates

I have following table

| ID | Name |StartDate |EndDate |
| -------- | -------- |
| 1 | Aa |2021-10-14 |2021-12-22 |
| 2 | Ab |2021-12-02 |2022-10-05 |

The requirement is to add new columns in YYYYMM format consisting of all the months between min(StartDate) and max(EndDate), and assign values to the corresponding cells. The cell value should be 1 if the date lies between StartDate and EndDate in that row, and should be 0 if it does not fall within that date range.The final output should be like in the below table

| ID | Name |StartDate |EndDate |202110|202111|202112|202201|202202|202203|202204|202205|202206|202207|
| -------- | -------- |
| 1 | Aa |2021-10-14 |2021-12-22 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | Ab |2021-12-02 |2022-07-05 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

For the 1st row, since the startdate=2021-10-14 & EndDate=2021-12-22, corresponding new columns should be 202110,202111 & 202112; and corresponding cell values are 1 for these columns while the other cells are 0. Same logic should be applied to other rows as well.

I could not figure out the logic to derive new tables with new columns and corresponding cell values.

How about this approach using dynamic SQL:

CREATE TABLE Data ( ID INT, Name VARCHAR(100), StartDate DATE, EndDate DATE )
INSERT Data
VALUES
('1', 'Aa', '2021-10-14', '2021-12-22'),
('2', 'Ab', '2021-12-02', '2022-10-05')
-- Extract overall date range
DECLARE @MinStartDate DATE, @MaxEndDate AS DATE
SELECT @MinStartDate = MIN(StartDate), @MaxEndDate =  MAX(EndDate)
FROM Data
-- Convert to months (DATETRUNC() may be used instead with SQL Server 2022 and later)
DECLARE @StartMonth DATE = DATEADD(day, 1 - DAY(@MinStartDate), @MinStartDate)
DECLARE @EndMonth DATE = DATEADD(day, 1 - DAY(@MaxEndDate), @MaxEndDate)
-- Generate calendar of months within range
DECLARE @Months TABLE ( Month DATE)
;WITH Months AS (
SELECT @StartMonth AS Month
UNION ALL
SELECT DATEADD(month, 1, M.Month)
FROM Months M
WHERE M.Month < @EndMonth
)
INSERT @Months
SELECT M.Month
FROM Months M
-- Define SQL Templates
DECLARE @SqlTemplate VARCHAR(MAX) = '
SELECT ID, Name, StartDate, EndDate
<ColumnSql>
FROM Data D
ORDER BY D.Name
'
DECLARE @ColumnTemplate VARCHAR(MAX) = '
, CASE WHEN D.StartDate <= <MonthEnd> AND <MonthStart> <= D.EndDate THEN 1 ELSE 0 END AS <ColumnName>'
-- Build month-specific column select items from template
DECLARE @ColumnSql VARCHAR(MAX) = (
SELECT STRING_AGG(C.ColumnSql, '') WITHIN GROUP(ORDER BY M.Month)
FROM @Months M
CROSS APPLY (
SELECT
CONVERT(CHAR(6), M.Month, 112) AS ColumnName,
M.Month AS MonthStart,
EOMONTH(M.Month) AS MonthEnd
) MD
CROSS APPLY (
SELECT REPLACE(REPLACE(REPLACE(
@ColumnTemplate
, '<ColumnName>', QUOTENAME(MD.ColumnName))
, '<MonthStart>', QUOTENAME(CONVERT(CHAR(8), MD.MonthStart, 112), ''''))
, '<MonthEnd>', QUOTENAME(CONVERT(CHAR(8), MD.MonthEnd, 112), ''''))
AS ColumnSql
) C
)
--SELECT @ColumnSql
-- Build final SQL
DECLARE @Sql VARCHAR(MAX) = REPLACE(@SqlTemplate, '<ColumnSql>', @ColumnSql)
SELECT @Sql
-- Deliver
EXEC (@Sql)

Generated SQL:

SELECT ID, Name, StartDate, EndDate
    , CASE WHEN D.StartDate <= '20211031' AND D.EndDate >= '20211001' THEN 1 ELSE 0 END AS [202110]
    , CASE WHEN D.StartDate <= '20211130' AND D.EndDate >= '20211101' THEN 1 ELSE 0 END AS [202111]
    , CASE WHEN D.StartDate <= '20211231' AND D.EndDate >= '20211201' THEN 1 ELSE 0 END AS [202112]
    , CASE WHEN D.StartDate <= '20220131' AND D.EndDate >= '20220101' THEN 1 ELSE 0 END AS [202201]
    , CASE WHEN D.StartDate <= '20220228' AND D.EndDate >= '20220201' THEN 1 ELSE 0 END AS [202202]
    , CASE WHEN D.StartDate <= '20220331' AND D.EndDate >= '20220301' THEN 1 ELSE 0 END AS [202203]
    , CASE WHEN D.StartDate <= '20220430' AND D.EndDate >= '20220401' THEN 1 ELSE 0 END AS [202204]
    , CASE WHEN D.StartDate <= '20220531' AND D.EndDate >= '20220501' THEN 1 ELSE 0 END AS [202205]
    , CASE WHEN D.StartDate <= '20220630' AND D.EndDate >= '20220601' THEN 1 ELSE 0 END AS [202206]
    , CASE WHEN D.StartDate <= '20220731' AND D.EndDate >= '20220701' THEN 1 ELSE 0 END AS [202207]
    , CASE WHEN D.StartDate <= '20220831' AND D.EndDate >= '20220801' THEN 1 ELSE 0 END AS [202208]
    , CASE WHEN D.StartDate <= '20220930' AND D.EndDate >= '20220901' THEN 1 ELSE 0 END AS [202209]
    , CASE WHEN D.StartDate <= '20221031' AND D.EndDate >= '20221001' THEN 1 ELSE 0 END AS [202210]
FROM Data D
ORDER BY D.Name

Results:

See this db<>fiddle.

The above uses a standard test for date range overlap of "start1 <= end2 AND start2 <= end1", which assumes all dates are inclusive.