Question

SELECT count(*), lower(name), number
FROM   tbl
GROUP  BY lower(name), number
HAVING count(*) > 1;

input tb1

slno name number
1    aaa   111
2    Aaa   111
3    abb   221
4    Abb   121
5    cca   131
6    cca   141
7    abc   222
8    cse   222

This query can just find the duplicates in the number and names which are same but it wont be able find the duplicates in the 3 and 4th row!!!

 SELECT count(*), lower(name)
    FROM   tbl
    GROUP  BY lower(name)
    HAVING count(lower(name)) > 1

this query can find all the duplicates in name!!! it works perfectly

 SELECT count(*), number
    FROM   tbl
    GROUP  BY number
    HAVING count(number) > 1

this query can find all the duplicates in number!!! it works perfectly

I want a query which can find all the duplicates in both name and number whether the name consists of lower case and upper case

output
name number count
2    111     aaa
2    ---     abb
2    ---     cca
2    222     ---

Answer 1

Updated question

"Get duplicate on both number and name" … "name and number as different column"
Rows can be counted twice here!

SELECT lower(name), NULL AS number, count(*) AS ct
FROM   tbl
GROUP  BY lower(name)
HAVING count(*) > 1

UNION  ALL
SELECT NULL, number, count(*) AS ct
FROM   tbl
GROUP  BY number
HAVING count(*) > 1;

-> sqlfiddle

Original question

The problem is that the query groups by

GROUP  BY lower(name), number

As row 3 and 4 have a different number, they are not the same for this query.

If you want to ignore different numbers for this query, try something like:

SELECT lower(name)
     , count(*) AS ct
FROM   tbl
GROUP  BY lower(name)
HAVING count(*) > 1;