Two typical options are:

select * from T t
where exists (
    select 1 from T t2
    where t2.Id = t.Id and t2.ProductName <> t.ProductName
);

with data as (
    select *, count(*) over (partition by Id) as cnt
    from T
)
select * from data where cnt > 1;

I reckon that, you had better to group the table without the having. The Query will be like the following:

select * 
from tbl1 
group by Id, ProductName

hope this solve your question

Below is one method to accomplish the task. The DISTINCT is not required with your sample data but is needed in case there are dups, which might be possible based on the sample data for other products.

SELECT DISTINCT Id, ProductName
FROM @Product
WHERE Id IN(
    SELECT Id
    FROM @Product
    WHERE ProductName = 'Product1'
    )
    AND Id IN(
    SELECT Id
    FROM @Product
    WHERE ProductName <> 'Product1'
    )
ORDER BY Id, ProductName;

Using COUNT(*) OVER (PARTITION BY Id) will give you the HAVING -like functionality.

WITH cte AS (
    SELECT Id,
           ProductName,
           NumProductsForId = COUNT(*) OVER (PARTITION BY Id),
           DoesIdContainDesiredProductName = MAX(CASE WHEN ProductName = 'Product1' THEN 1 END) OVER (PARTITION BY Id)
    FROM tbl1
)
SELECT Id, ProductName
FROM cte
WHERE NumProductsForId > 1
  AND DoesIdContainDesiredProductName = 1;