How to do a case sensitive GROUP BY?

Simply:

SELECT count(*), CAST(lastname as BINARY) AS lastname_cs 
FROM names 
GROUP BY lastname_cs; 

You can use an case sensitive collation:

with temp as
(
  select 'Test' COLLATE Latin1_General_CS_AS as name
  UNION ALL
  select 'TEST'
  UNION ALL
  select 'test'
  UNION ALL
  select 'tester'
  UNION ALL
  select 'tester'
)
SELECT name, COUNT(name)
FROM temp
group by name

You need to cast the text as binary (or use a case-sensitive collation).

With temp as
(
  select 'Test' as name
  UNION ALL
  select 'TEST'
  UNION ALL
  select 'test'
  UNION ALL
  select 'tester'
  UNION ALL
  select 'tester'
)
Select Name, COUNT(name)
From temp
Group By Name, Cast(name As varbinary(100))

Using a collation:

Select Name Collate SQL_Latin1_General_CP1_CS_AS, COUNT(name)
From temp
Group By Name Collate SQL_Latin1_General_CP1_CS_AS