SQL> create table tbl(n number)
  2  /

Table created.

SQL> create index tbl_idx1
  2    on tbl(n)
  3  /

Index created.

SQL> alter table tbl
  2    add constraint tbl_uk
  3      unique(n)
  4  /

Table altered.

SQL> select index_name
  2    from user_constraints
  3    where constraint_name = 'TBL_UK'
  4  /

INDEX_NAME
--------------------------------------------------------------------------------
TBL_IDX1

SQL>  insert into tbl
  2    values(1)
  3  /

1 row created.

SQL> /
insert into tbl
*
ERROR at line 1:
ORA-00001: unique constraint (SCOTT.TBL_UK) violated


SQL>