After some more research it looks like some kind of version problem.
We have two severs. The first is Oracle 8.04 and the second is Oracle 8.17, both on different NT 4.0 server machines.
If I try to connect with SQLPlus on the 8.04 server it must be the "xxx.world" format, otherwise the ORA-12154 error occurs.
My computer has the 8.17 client installed. So far I had no problems at all connecting and working with 8.04. My tnsnames.ora has its entries in format "xxx". If I change it to format "xxx.world" ORA-12154 occurs again.
It seems like Oracle 8.0x needs the ".world" format and 8i needs the "xxx" format or said in other words for 8i these are two different aliases.
If I use a TEdit instead of the OracleAliasList and type in the exact alias name "xxx" or "xxx.world" I can connect successfully. This works exactly the same way for SQLPlus and my DOA application.
True, who will need different server and client versions? But if ".world" would not be cut in the OracleAliasList it seems like this strange problem could be avoided.