Hi,

I don't believe renewing your passport will solve the issue, because you have the same name.
You can come to visit if you a resident of any GCC country, or work for another company in GCC who can lend your services to another company in Qatar.
Or complete the 2 years, then you can come back to work in Qatar.

This ban is an extremely an unjust rule, especially when companies end employment contracts without any faults by the employees in some cases, and on top of that refuse to grant this NOC letter.

This rule was lifted completely in the UAE to make people's lives easier after experiencing similar unfair practices by companies against employees.