Interesting, I didn't know that!
The forth argument of instr allows you to find the Nth occurrence of the string. So you could look for the second instance of parentheses:
with errmsg as (
select 'ORA-00001: a(z) (CHRIS.SYS_C009827) egyediségre vonatkozó megszorítás nem teljesül' e
from dual
)
select substr( e, instr(e, '(', 1, 2)+1,
instr( e, ')', 1, 2) - instr( e,'(', 1, 2) -1 ) c
from errmsg;
C
CHRIS.SYS_C009827