Go to the URL below(*) and search for the chapter “Updating ORACLE_SID in the Registry”. It explains how to set a default Oracle database under Windows OS.
Don’t know how to do it under Unix. I advise you to perform a search over the OTN website.
(*) possibly you will be asked to log-on to Oracle’s OTN website – if you don’t have an account yet, create one as OTN is a repository of valuable info about Oracle.