How to extract names from varchar column in SQL Server ?

Try with below queries:

Query to Fetch records with star

SELECT usr.id, user.name FROM User usr
INNER JOIN Summary smr
ON usr.id = smr.id
WHERE smr.summary LIKE '%*'

Query to Fetch records without star

SELECT usr.id, user.name FROM User usr
INNER JOIN Summary smr
ON usr.id = smr.id
WHERE smr.summary LIKE '%[^*]'

1. Query for get record with *

select id,name from users u inner join summary s
on u.id=s.id
where summary  like '%*'

2. Query for get record without  *

select id,name from users u inner join summary s
on u.id=s.id
where summary  not like '%*'

Here is a way of getting the results you require.

Using like to find the corresponding names in summary.
Then getting the charindex of the name and the star * position after the name.
Using a bit of lead over to figure out if a star exists after the name but not before the next name in the summary.

Here is a cte query of how it can be done:

with Summary as(
--setup dummy data
	select 1 id,'asdffgggggg Anand   * edkkofffmfmmfmfm Bala          sdkdodkekeke Chandra dkkdkd "vinoth"*' summary
	union all select 2, 'asdffgggggg Dinesh  * edkkofffmfmmfmfm Frankin       sdkdodkekeke Elisia  dkkdkd  Ganesh.'
	union all select 3, 'asdffgggggg Hansika  edkkofffmfmmfmfm [A.Ishwariya]* sdkdodkekeke Jack    dkkdkd "Lalitha"'
), Name as (
	select 1 id,'A.Ishwariya' name
	union all select 2 id,'Anand'
	union all select 3 id,'Bala'
	union all select 4 id,'Chandra'
	union all select 5 id,'Dinesh'
	union all select 6 id,'Elisia'
	union all select 7 id,'Frankin'
	union all select 8 id,'Ganesh'
	union all select 9 id,'Hansika'
	union all select 10 id,'Jack'
	union all select 11 id,'Lalitha'
	union all select 12 id,'Vinoth'
), SummaryName as (
	select
		s.id SummaryId,
		s.summary,
		n.id NameId,
		n.name,
		lead(s.id) over(order by s.id) NextSummaryId,
		len(s.summary) LenSummary
	from Summary s
	inner join Name n
		on	s.summary like '%'+n.name+'%'
), SummaryNameStarPos as (
	select 
		top(1000)
		*,
		charindex(sn.name, sn.summary) NmPos,
		charindex('*', sn.summary, charindex(sn.name, sn.summary)) NextStarPos,
		isnull(lead(charindex(sn.name, sn.summary)) over(order by SummaryId, charindex(sn.name, sn.summary)), 0) NextNmPos
	from SummaryName sn
	--order by
	--	sn.SummaryId,
	--	NmPos
)
select
	*
from SummaryNameStarPos


--name with star
where NextStarPos > NmPos
and (NextStarPos < NextNmPos or (NextSummaryId <> SummaryId and NextStarPos <= LenSummary))

--name without star
where not (NextStarPos > NmPos
	and (NextStarPos < NextNmPos or (NextSummaryId <> SummaryId and NextStarPos <= LenSummary))
)

It works with the sample data you have supplied.
You may need to modify the where clauses a little with the original data, but you should be able to see what is being compared to get the final results.
Ensure the records are ordered correctly, where they should be ordered by summary and name position, otherwise the lead over will not work as expected.

Probably not an efficient way of doing it.
Also take into consideration of advise from solution 1 of splitting out the summary data.

Hope that helps out.