Cómo usar una columna temporal en la cláusula where

Usa HAVING en cambio:

Select
    product_brand,
    (CASE WHEN COUNT(product_brand)>50 THEN 1 ELSE 0 END) AS brand_count
  FROM products
  GROUP BY product_brand
  HAVING brand_count = 1

WHERE se evalúa antes el GROUP BY . HAVING se evalúa después.