MySQL pivot row into dynamic number of columns

Unfortunately MySQL does not have a PIVOT function which is basically what you are trying to do. So you will need to use an aggregate function with a CASE statement:

select pt.partner_name,
  count(case when pd.product_name = 'Product A' THEN 1 END) ProductA,
  count(case when pd.product_name = 'Product B' THEN 1 END) ProductB,
  count(case when pd.product_name = 'Product C' THEN 1 END) ProductC,
  count(case when pd.product_name = 'Product D' THEN 1 END) ProductD,
  count(case when pd.product_name = 'Product E' THEN 1 END) ProductE
from partners pt
left join sales s
  on pt.part_id = s.partner_id
left join products pd
  on s.product_id = pd.prod_id
group by pt.partner_name

See SQL Demo

Since you do not know the Products you will probably want to perform this dynamically. This can be done using prepared statements.

With dynamic pivot tables (transform rows to columns) your code would look like this:

SET @sql = NULL;
SELECT
  GROUP_CONCAT(DISTINCT
    CONCAT(
      'count(case when Product_Name = ''',
      Product_Name,
      ''' then 1 end) AS ',
      replace(Product_Name, ' ', '')
    )
  ) INTO @sql
from products;

SET @sql = CONCAT('SELECT pt.partner_name, ', @sql, ' from partners pt
left join sales s
  on pt.part_id = s.partner_id
left join products pd
  on s.product_id = pd.prod_id
group by pt.partner_name');

PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

See SQL Demo

It's probably worth noting that GROUP_CONCAT is by default limited to 1024 bytes. You can work around this by setting it higher for the duration of your procedure, ie. SET @@group_concat_max_len = 32000;