Hi, is it possible to set a multiplayer match with mission?
Or is it always "conquer the world"?

Generally speaking it is conquer the world. You could add commanders (https://www.warzone.com/wiki/Commanders) but that doesn't change a whole lot.

But having custom mission would require a mod or just play by gentlemans rules and have the other players surrender when the "mission" is completed.

You can use Custom Scenarios as well.

Technically, you can add any rules you want into the game by writing them to the game description. Without mod, you have no way how to force players to play according to your rules. Nevertheless, if you write in the level name that it has special rules, majority of players should follow them. If they don't, you can blocklist these players, create a new game and invite there players who followed the rules.

If "Gentlemen's Rules" is appropriate, anything goes tbh.

There's also the mod that allows for alternate win conditions which could help somewhat.