What will happen to actual coins in desktop wallet or other wallet after rebranding?
There will be only name change or some fork?
Will the new brand still have 19 million max supply and so on or it will be new coin and mining from scratch?

Most what i want know is what will happen to my bought coins in wallet and parked in bank. Or its just desing rebrand?

I think Minexcoin and MNX is ok name. Its just synonym for saving money in crypto world, like in real world there are many saving banks/insurance company. In crypto is this saving bank or insurance called Minexcoin company (or Minexsystems company which offer the saving in crypto world through their product MNX).