SQL & PL/SQL

I am trying to use a subquery within a Case statement with a 'where' condition that binds to the parent query. Like this:

Select T.idperson , CASE WHEN  T.type = 'C' THEN (SELECT name from Customers where C.idcustomer = T.idperson) 
ELSE
 (SELECT name from Providers where idprovider = T.idperson)
 END Name 
from myTable T 

This works for me in SQL Server but in ORACLE the subquery does not return any rows, i guess its the binding to parent query part. Any thoughts of another way I could get the result I want?

Thanks,

JuanDiego