How to get count for different columns on same table
It's easiest with SUM() and a CASE statement:

select CompanyName, 
sum(case when StatusID=1 then 1 else 0 end) as TotalOpenClaims,
sum(case when StatusID=2 then 1 else 0 end) as TotalClosedClaims,
sum(case when StatusID=3 then 1 else 0 end) as TotalReOpenedClaims,
sum(case when StatusID=4 then 1 else 0 end) as TotalPendingClaims
from Claims
group by CompanyName;