I use it a LOT.
Usually to denote player values within the squad. (I.E - Joe Bloggs* / John Brown***)
Every now and then, a player will get a nickname due to something that has happened to them in the FM World.
(My Goals Scorer is now called Pele + No. of goals he's currently scored. (950, despite what my Location says

) - So Pele 950.
I dubbed one player "The Departed" after his 3rd spell at my club, and 7th club overall.
I had another kid who had a very difficult name to read, so I took a few letters from it and called him "Kviskvinho"
Also, if some players have really cool surnames, I'll just use the nickname feature to give them the surname as the name. (Tony Mulvenna became Mulvenna, and so on)