sql One-many and one-one relation between columns - sql-server

Question

I have no idea if the title matches what I am trying to achieve in the query given below. The example might not be great but it serves what I am trying to achieve. There are three results that I am trying to get as shown below. Can this be done with a single query showing all the results in a better way?
TABLE:
name surname gender
arjun khadka female
arjun khadka male
arjun basnet male
kumar khadka female
kumar basnet female
arjun khadka female
arjun basnet female
kumar khadka female
query:
WITH cte
AS (SELECT
*,
DENSE_RANK() OVER (ORDER BY name, surname) AS groupid1,
DENSE_RANK() OVER (ORDER BY name, surname, gender) AS groupid2
FROM (SELECT
name,
surname,
gender
FROM name) x)
same person with duplicate gender as well as with non duplicate
gender
SELECT
name,
surname,
gender
FROM CTE
WHERE groupid1 IN (SELECT
groupid1
FROM cte
GROUP BY groupid1,
groupid2
HAVING COUNT(*) > 1)
AND groupid1 IN (SELECT
groupid1
FROM cte
GROUP BY groupid1,
groupid2
HAVING COUNT(*) = 1)
same person with no duplicate gender at all
SELECT
*
FROM cte
WHERE groupid1 NOT IN (SELECT
groupid1
FROM cte
GROUP BY groupid1,
groupid2
HAVING COUNT(*) > 1)
same person having duplicate gender record only
SELECT
*
FROM cte
WHERE groupid1 IN (SELECT
groupid1
FROM cte
GROUP BY groupid1,
groupid2
HAVING COUNT(*) > 1)
AND groupid1 NOT IN (SELECT
groupid1
FROM cte
GROUP BY groupid1,
groupid2
HAVING COUNT(*) = 1)
I modified what #uzi has provided, as solution as it has some flaws:
select
distinct name, surname,personCount as count
, personHasDupNUniqueGender = iif(min(allRowsCount) over (partition by personGroupId) = 1 and max (allRowsCount) over (partition by personGroupId) >1,1,0)
, personHasUniqueGender = iif(max(allRowsCount) over (partition by personGroupId) = 1,1,0)
, personHasAllDupGender = iif(personCount = allrowscount and personcount>1,1,0)
from (
select
*
, personGroupId= DENSE_RANK() over (order by name, surname)
, personCount = count(*) over (partition by name, surname)
, allRowsCount = count(*) over (partition by name, surname, gender)
from
name
) t
order by name, surname

Answer 1

Here's one way. Query returns all rows with extra columns condition_1, condition_2, condition_3. Values of those columns either 1 or 0. 1 - matches condition
declare #t table (
name varchar(100)
, surname varchar(100)
, gender varchar(100)
)
insert into #t values
('arjun', 'khadka', 'female')
,('arjun', 'khadka', 'male')
,('arjun', 'basnet', 'male')
,('kumar', 'khadka', 'female')
,('kumar', 'basnet', 'female')
,('arjun', 'khadka', 'female')
,('arjun', 'basnet', 'female')
,('kumar', 'khadka', 'female')
select
name, surname, gender
, condition_1 = max(iif(cnt_1 = 1 and cnt_2 > 2, 1, 0)) over (partition by name, surname)
, condition_2 = iif(cnt_2 - cnt_1 <= 1 and cnt_1 = 1, 1, 0)
, condition_3 = iif(cnt_2 = cnt_1 and cnt_1 > 1, 1, 0)
from (
select
*, cnt_1 = count(*) over (partition by name, surname, gender)
, cnt_2 = count(*) over (partition by name, surname)
from
#t
) t
order by name, surname
Output
name surname gender condition_1 condition_2 condition_3
-------------------------------------------------------------------
arjun basnet female 0 1 0
arjun basnet male 0 1 0
arjun khadka female 1 0 0
arjun khadka female 1 0 0
arjun khadka male 1 0 0
kumar basnet female 0 1 0
kumar khadka female 0 0 1
kumar khadka female 0 0 1
Edit:
select
name, surname, gender, cnt_1, cnt_2
, condition_1 = max(iif(cnt_1 = 1 and cnt_2 > 2, 1, 0)) over (partition by name, surname)
, condition_2 = iif(max(cnt_1) over (partition by name, surname) = 1, 1, 0)
, condition_3 = iif(cnt_2 = cnt_1 and cnt_1 > 1, 1, 0)
from (
select
*, cnt_1 = count(*) over (partition by name, surname, gender)
, cnt_2 = count(*) over (partition by name, surname)
from
#t
) t
order by name, surname