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 My Team tab, then press Customize Team:
If your league is in pre-draft mode you won't have a My Team tab just yet, but you can go to your league homepage and scroll down to the list of teams in the league and click on yours. Then you'll see another Customize Team option.
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."