Could not resolve service name simply means that the Oracle client does not know of a server or instance by the name you've given.
Check it at a command prompt using
If that works, then you know the service is configured properly. If not, have a look in a file called TNSNAMES.ORA located somewhere under c:\oracle (or wherever you installed the oracle client).
All of the various instances and names will be in there. If you can't find your instance named in there, then copy the tnsnames.ora entry from another machine that has got a correct entry, or copy & paste an existing entry and make the necessary changes.
Use something like SqlPlus to confirm your client etc is configured correctly, once you've done that, then try to get Delphi connecting.