The standard regexp solution is to look for substrings of ZERO or more non-delimiters (instead of ONE or more), followed by a comma or the end-of-string. This last part is the only subtle bit (and the only reason for the more complicated regexp, using backreferences); without it, [^,]* would also match empty substrings after each nonempty one.

with
  input_string (my_string) as (
    select 'Jagjit,,Jane,Harinder,,Alice'
    from    dual
  )
select regexp_substr(my_string, '([^,]*)(,|$)', 1, 1, null, 1) as name1,
       regexp_substr(my_string, '([^,]*)(,|$)', 1, 2, null, 1) as name2,
       regexp_substr(my_string, '([^,]*)(,|$)', 1, 3, null, 1) as name3,
       regexp_substr(my_string, '([^,]*)(,|$)', 1, 4, null, 1) as name4,
       regexp_substr(my_string, '([^,]*)(,|$)', 1, 5, null, 1) as name5,
       regexp_substr(my_string, '([^,]*)(,|$)', 1, 6, null, 1) as name6
from   input_string
;

NAME1     NAME2     NAME3     NAME4     NAME5     NAME6    
--------- --------- --------- --------- --------- ---------
Jagjit              Jane      Harinder            Alice   

@Chris - that method has one structural weakness, and the implementation is deficient as well.

Let's start with the implementation: substituting comma-space-comma for two consecutive commas will not account for NULL tokens right at the beginning of the string (that is: a string that begins with a comma, indicating the FIRST token is NULL), and also for NULL tokens right at the end. It will also not account for two consecutive NULL tokens in the string (like 'Alice,,,Dan,Emma,Flor') - a space will be added between the first and second comma, but not between the second and the third.

In all these cases, the output from the query, as written, will be wrong (there will be no error thrown to alert us to anything; the output will just be incorrect). They can be fixed, but the query becomes even more complicated.

The structural issue is more serious though. In the most general case, the tokens don't have to be "names", they can be any valid strings. If a single space is a valid NON-NULL token (a string of length 1), this approach will destroy that distinction. This can also be fixed - use a control character (like CHR(7), the system bell - assuming this is not a "valid" character in the inputs) as a marker for NULL - and then replace it back with "nothing" after the splitting.

Using subexpression in regular expression:-
WITH input_string AS (
SELECT 'Jagjit,,Jane,Harinder,,Alice' AS my_string
, '([^,]*),?' AS regex --Part in brackets is the subexpression "any non comma character", followed by an optional comma
FROM dual
)
SELECT
--the final ,1 gets the subexpression inside commas (in other words remove the comma it matches).
REGEXP_SUBSTR(my_string, regex, 1, 1,'',1) Name1
, REGEXP_SUBSTR(my_string, regex, 1, 2,'',1) Name2
, REGEXP_SUBSTR(my_string, regex, 1, 3,'',1) Name3
, REGEXP_SUBSTR(my_string, regex, 1, 4,'',1) Name4
, REGEXP_SUBSTR(my_string, regex, 1, 5,'',1) Name5
, REGEXP_SUBSTR(my_string, regex, 1, 6,'',1) Name6
FROM input_string;


Alternatively, consider APEX_STRING

SELECT *
FROM APEX_STRING.split ('Jagjit,,Jane,Harinder,,Alice',',')

I found this method in AskTom while ago and been using it ever since. No regexp necessary:)

WITH input_strings AS
 (SELECT 'Jagjit,,Jane,Harinder,,Alice' input_string
    FROM dual),
strings AS
 (SELECT TRIM(substr(txt, instr(txt, ',', 1, LEVEL) + 1, instr(txt, ',', 1, LEVEL + 1) - instr(txt, ',', 1, LEVEL) - 1)) serving_result
    FROM (SELECT ',' || input_strings.input_string || ',' txt
            FROM input_strings)
        ,input_strings
  CONNECT BY LEVEL <= length(input_strings.input_string) - length(REPLACE(input_strings.input_string, ',', '')) + 1)
SELECT *
  FROM strings;

I realize the question says version 12.1.0.2, but I hope anyone who has the same question using a more recent version will consider using SQL/JSON - as a first step toward replacing all those CSV strings with JSON arrays!

with data(x) as (
  select '' from dual union all
  select ',' from dual union all
  select ',,' from dual union all
  select ',,,' from dual union all
  select ',,c' from dual union all
  select ',,c,' from dual union all
  select ',b' from dual union all
  select ',b,' from dual union all
  select ',b,,' from dual union all
  select ',b,c' from dual union all
  select ',b,c,' from dual union all
  select 'a' from dual union all
  select 'a,' from dual union all
  select 'a,,' from dual union all
  select 'a,,,' from dual union all
  select 'a,,c' from dual union all
  select 'a,,c,' from dual union all
  select 'a,b' from dual union all
  select 'a,b,' from dual union all
  select 'a,b,,' from dual union all
  select 'a,b,c' from dual union all
  select 'a,b,c,' from dual union all
  select 'a,b,c,d' from dual
)
select nvl(x, '(null)') x, 
  nvl(a, '(null)') a,
  nvl(b, '(null)') b,
  nvl(c, '(null)') c,
  nvl(d, '(null)') d
from data, json_table(
  replace(json_array(x), ',', '","'), '$' columns
  a path '$[0]',
  b path '$[1]',
  c path '$[2]',
  d path '$[3]'
);

X          A         B         C         D         
(null)     (null)    (null)    (null)    (null)    
,          (null)    (null)    (null)    (null)    
,,         (null)    (null)    (null)    (null)    
,,,        (null)    (null)    (null)    (null)    
,,c        (null)    (null)    c         (null)    
,,c,       (null)    (null)    c         (null)    
,b         (null)    b         (null)    (null)    
,b,        (null)    b         (null)    (null)    
,b,,       (null)    b         (null)    (null)    
,b,c       (null)    b         c         (null)    
,b,c,      (null)    b         c         (null)    
a          a         (null)    (null)    (null)    
a,         a         (null)    (null)    (null)    
a,,        a         (null)    (null)    (null)    
a,,,       a         (null)    (null)    (null)    
a,,c       a         (null)    c         (null)    
a,,c,      a         (null)    c         (null)    
a,b        a         b         (null)    (null)    
a,b,       a         b         (null)    (null)    
a,b,,      a         b         (null)    (null)    
a,b,c      a         b         c         (null)    
a,b,c,     a         b         c         (null)    
a,b,c,d    a         b         c         d 

Best regards,
Stew

A reader mentioned an INSTR&SUBSTR solution that generates one row per item. This is a way to get multiple columns on one line; maybe it's easier to understand than REGEX?

with data(x) as (
  select '' from dual union all
  select ',' from dual union all
  select ',,' from dual union all
  select ',,,' from dual union all
  select ',,c' from dual union all
  select ',,c,' from dual union all
  select ',b' from dual union all
  select ',b,' from dual union all
  select ',b,,' from dual union all
  select ',b,c' from dual union all
  select ',b,c,' from dual union all
  select 'a' from dual union all
  select 'a,' from dual union all
  select 'a,,' from dual union all
  select 'a,,,' from dual union all
  select 'a,,c' from dual union all
  select 'a,,c,' from dual union all
  select 'a,b' from dual union all
  select 'a,b,' from dual union all
  select 'a,b,,' from dual union all
  select 'a,b,c' from dual union all
  select 'a,b,c,' from dual union all
  select 'a,b,c,d' from dual
)
select x,
  substr(x,           1, after_a           - 1) a,
  substr(x, after_a + 1, after_b - after_a - 1) b,
  substr(x, after_b + 1, after_c - after_b - 1) c,
  substr(x, after_c + 1, after_d - after_c - 1) d
from (
  select x,
    instr(x||',', ',', 1, 1) after_a,
    instr(x||',', ',', 1, 2) after_b,
    instr(x||',', ',', 1, 3) after_c,
    instr(x||',', ',', 1, 4) after_d
  from data
);

Same results as above.

Regards,
Stew