I dont think it makes much difference for managers who wants more matches what name the competition will be given.

The easiest way will be for Nordeus to create 2 competitions; 1 when the first bunch of managers get kicked out of cup/CL and 2nd competition when the last bunch get kicked out of the competitions. Example: 1st competition starts after the cup eliminations and 2nd after CL top 16

Some people think football is a matter of life and death. I assure you, it's much more serious than that.