SQL> ed
Wrote file afiedt.buf

  1  with ww as
  2  (select 1 n, 'OM.test11 omega.test12 test' s from dual
  3  union all
  4  select 2 n, 'OM.kuke test' s from dual
  5  union all
  6  select 3 n, 'OM kuomke testom' s from dual
  7  )
  8  select n, regexp_substr(s, '(\S*)om(\S*)', 1, level, 'i') tablename, level
  9  from ww
 10  connect by regexp_substr(s, '(\S*)om(\S*)', 1, level, 'i') is not null
 11   AND PRIOR n = n
 12   AND PRIOR dbms_random.value IS NOT NULL
 13* order by 1,3
SQL> /

         N TABLENAME                        LEVEL
---------- --------------------------- ----------
         1 OM.test11                            1
         1 omega.test12                         2
         2 OM.kuke                              1
         3 OM                                   1
         3 kuomke                               2
         3 testom                               3

6 rows selected.

SQL>

 1  with ww as
  2  (select 1 n, 'OM.test11 omega.test12 test' s from dual
  3  union all
  4  select 2 n, 'OM.kuke test' s from dual
  5  union all
  6  select 3 n, 'OM.kuke.test' s from dual
  7  union all
  8  select 4 n, 'O M kuomke testom' s from dual
  9  union all
 10  select 5 n, ' OM kuomke testom' s from dual
 11  union all
 12  select 6 n, '' s from dual
 13  )
 14* select ww.*,substr(s,1,instr(s,' ')-1) s1 from ww
SQL> /

         N S                           S1
---------- --------------------------- ---------------------------
         1 OM.test11 omega.test12 test OM.test11
         2 OM.kuke test                OM.kuke
         3 OM.kuke.test                null
         4 O M kuomke testom           O
         5  OM kuomke testom           null
         6 null                        null

6 rows selected.