This is not the most elegant way of doing it and to be honest this kind of things should really be done in the presentation layer (e.g. in your report) but anyway..

You can just UNION the year totals in your subquery can fix the name as 'Total' then just add this new month to the pivot expression.

drop table if exists #sales
create table #sales(
  itemcode INT, name varchar(255), amount decimal(18,2), salesdate date);
insert into #sales (itemcode, name, amount, salesdate) values (01, 'product1', 01, '2023-10-01'),
(01, 'product1', 5, '2023-11-03'),
(02, 'product1', 10, '2023-11-10')

SELECT * 
  FROM (
       SELECT YEAR(SalesDate) [YEAR], 
              DATENAME(MONTH, SalesDate) [Month], 
              COUNT(1) [Amount Count], 
              itemcode, 
              Name 
       FROM #Sales
       GROUP BY YEAR(SalesDate), DATENAME(MONTH, SalesDate), itemcode, Name
       UNION ALL 
       SELECT YEAR(SalesDate) [YEAR], 
              'Total' [Month], 
              COUNT(1) [Amount Count], 
              itemcode, 
              Name 
       FROM #Sales
       GROUP BY YEAR(SalesDate), itemcode, Name  
       ) AS MonthlyDates
  PIVOT (SUM([Amount Count])
   FOR MONTH IN ([January],[February],[March],[April],[May],
      [June],[July],[August],[September],[October],[November],
      [December],
      [Total])
  ) as MNAMEPIVOT

Here's the result

One solution is to extract the month from the salesdate variable, and then use a GROUP BY function to sum up the sales amount by month.

Firstly, a separate variable can be created as follows:

alter table sales add month int;

The month can then be extracted:

update sales set month=extract(month from salesdate);

Sales can then be grouped by month and name. Based on the sample data you provided, the results are as follows:

select month, name, sum(amount)
from sales
group by month, name
order by month;

month |   name   |  sum  
-------+----------+-------
    10 | product1 |  1.00
    11 | product1 | 15.00
(2 rows)