[oracle@test oracle]$ ORACLE_SID= newsid
[oracle@test oracle]$ export ORACLE_SID

[oracle@test oracle]$ echo $ORACLE_SID
newsid


Also, just as a word of advice. If you plan on creating more than one oracle database on that box I would advise on creating different userids instead of just oracle. That way you'll be able to tell right off the bat who's doing what on that box instead of seeing a bunch of processes with the oracle userid.