You’ll be able to acquire new emblems and nicknames primarily by participating in multiplayer matches though some nicknames are available for meeting various conditions while playing in campaign as well. After completing the campaign once, you’ll be able to equip emblems to your planes in campaign.
After selecting your emblem, you'll have the choice to apply it on your aircraft's nose, tail, or wing. Unfortunately, you can't manually change the exact positions of the emblems but you can at least toggle its application on or off in the specified parts of your plane.
You can assign a nickname to an aircraft set and you can freely modify it. Your nickname will be visible to the other players and what will appear during the intro/outro of each match as well.
Here are some of the conditions to unlock a new nickname: