What is the ruling regarding someone who prayed Jumu'ah for years with the intention of Dhuhr or Jumu'ah Dhuhr due to his ignorance of its correct designation, despite his knowledge that it is only two rak'ahs? And what is the validity of praying Dhuhr four rak'ahs after Jumu'ah prayer, claiming that Jumu'ah is an independent prayer?

The fundamental principle is that the intention for Jumu'ah (Friday prayer) is obligatory. Whoever intends to pray Dhuhr (noon prayer) will not have that suffice for Jumu'ah.

However, if the worshippers intended Jumu'ah with their prayer—even if they were unaware of its specific naming—their prayer is valid, God willing, because the intention for the obligatory prayer of the time is sufficient.

As for re-praying Dhuhr after Jumu'ah, this is an innovation that must be avoided.