SQL Server 2012

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declare @now date = sysdatetime()
	,@day_count int = 10;
with cte  as (
	select 1 val,dateadd(day,1,@now) [date]
	union all
	select t2.val +1 as val,dateadd(day,t2.val+1,@now) from (select 1 val) t1 
	inner join cte t2 on t2.val < @day_count 
)
select 
	[date],datename(weekday,[date])  as [weekday name]
from cte;


date
weekday name


17/01/2020 00:00:00
Friday

18/01/2020 00:00:00
Saturday

19/01/2020 00:00:00
Sunday

20/01/2020 00:00:00
Monday

21/01/2020 00:00:00
Tuesday

22/01/2020 00:00:00
Wednesday

23/01/2020 00:00:00
Thursday

24/01/2020 00:00:00
Friday

25/01/2020 00:00:00
Saturday

26/01/2020 00:00:00
Sunday


create function dbo.getnext10days(@fromdate date)
returns table as return
with cte  as (
	select 1 val,dateadd(day,1,@fromdate) [date]
	union all
	select t2.val +1 as val,dateadd(day,t2.val+1,@fromdate) from (select 1 val) t1 
	inner join cte t2 on t2.val < 10 
)
select 
	[date],datename(weekday,[date])  as [weekday name]
from cte;
select * from dbo.getnext10days('2020/01/01')


date
weekday name


02/01/2020 00:00:00
Thursday

03/01/2020 00:00:00
Friday

04/01/2020 00:00:00
Saturday

05/01/2020 00:00:00
Sunday

06/01/2020 00:00:00
Monday

07/01/2020 00:00:00
Tuesday

08/01/2020 00:00:00
Wednesday

09/01/2020 00:00:00
Thursday

10/01/2020 00:00:00
Friday

11/01/2020 00:00:00
Saturday

date	weekday name
17/01/2020 00:00:00	Friday
18/01/2020 00:00:00	Saturday
19/01/2020 00:00:00	Sunday
20/01/2020 00:00:00	Monday
21/01/2020 00:00:00	Tuesday
22/01/2020 00:00:00	Wednesday
23/01/2020 00:00:00	Thursday
24/01/2020 00:00:00	Friday
25/01/2020 00:00:00	Saturday
26/01/2020 00:00:00	Sunday

date	weekday name
02/01/2020 00:00:00	Thursday
03/01/2020 00:00:00	Friday
04/01/2020 00:00:00	Saturday
05/01/2020 00:00:00	Sunday
06/01/2020 00:00:00	Monday
07/01/2020 00:00:00	Tuesday
08/01/2020 00:00:00	Wednesday
09/01/2020 00:00:00	Thursday
10/01/2020 00:00:00	Friday
11/01/2020 00:00:00	Saturday