Determine total number of aggregate weeks excluding overlap periods

I have query which returns thousands of rows, with a number and name, fromdate and today. I need to calculate the total number of aggregate weeks but exclude the overlapping date range. I have not been able to find a way.

As you can see, the 7th row of data is 2018-09-12 and next starting date is 2018-09-08. All of these rows is only for one number, but in other number columns, there are a lot more overlaps but example is the same. I have to exclude these overlaps. e.g. in another example, row one is the whole month of January, and row two is a week from 10 to 17th in it. so this is another example.

I tried to do a self join on the table but could not figure it out.

select *
from #RW r1, #RW r2
where r1.number = r2.number and r1.name = r2.name 
and r1.Fromdate < r2.Fromdate and r1.todate > r2.Fromdate 
and r1.number = '887' 

**NOTE: If daycount = 0 , then that row should be ignored. it was generated based on another condition before I exported.

Desired output:
the desired result set would be to have a new result set (with consecutive date ranges) excluding the date overlaps. e.g. in above example, I want to remove the dates from 2018-09-08 until 2018-09-11 as these 4 days are already covered by the row above it. So naturally it should be all rows showing based on chronologica order, with merged fromdate/todate. as you can see, there are gaps between dates and I can't go with Min(fromdate) | Max(todate).

Thanks in advance for your help,

Here's my solution with recursive CTE

;WITH cteGeneratedDates AS (
        SELECT
			number,
			[name],
			fromdate,
			todate
		FROM TableName
		WHERE fromdate IS NOT NULL 
			AND daycount > 0 -- comment this out if 0 daycount should be counted

        UNION ALL
		SELECT
			number,
			[name],
			fromdate = DATEADD(DAY, 1, fromdate),
			todate
        FROM cteGeneratedDates
		WHERE DATEADD(DAY, 1, fromdate) <= todate
),
cteGroupedConsecutiveDates AS (
	SELECT
		number,
		[name],
		fromdate,
		ROW_NUMBER() OVER (PARTITION BY number, [name] ORDER BY fromdate) todate
	FROM cteGeneratedDates
	GROUP BY number, [name], fromdate
)
SELECT 
	number,
	[name],
	MIN(fromdate) fromdate,
	MAX(fromdate) todate,
	DATEDIFF(DAY, MIN(fromdate), MAX(fromdate))
FROM cteGroupedConsecutiveDates
GROUP BY
	number,
	[name],
	DATEDIFF(DAY, fromdate, todate)
ORDER BY fromdate
OPTION (MAXRECURSION 2000)

Though there's difference with your expected output because of the following: why do these groups not grouped under 1 row?

• 03/11/2021 - 02/03/2022
• 03/03/2022 - 30/03/2022
• 31/03/2022 - 05/07/2023

In my solution, above ranges would be in the same group.

Also, there are no dates between 07/11/2018 and 28/11/2018, don't you think this group needs to be broken down? 30/05/2018 - 29/05/2019