Player nicknames are a way for users to customize the names of the players they own.
Many users utilize this feature to give players funny names and others use it for a note or salary of that player.
On the Web App
Using the web app, you can go to the Team tab, then click on the settings icon to the right of your team to get to this screen:
On the Mobile App
Go to your specific league and press the settings icon in the top right. Then, press on the tile labeled "My Team."