This should work. I think you were pretty close but the RC one is a little bit more difficult.
select Name,
case
when Max(id) < 4 then 'R'
when MAX(id) = 4 and min(id) = 4 then 'C'
when min(id) < 4 and exists(select * from tblTestId t2 where id = 4 and t2.Name = t.Name) then 'RC'
end as [Status]
from tblTestId t
group by Name
order by Name
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