Tap the menu on the left-sidebar. If you can't see the sidebar, tap the button at the top right corner.
Just tap the player information button on the menu screen.
Now you can see your current player rank, required exp to next rank, player name, affiliated guild, player id, and comment.
Tap the change name button on the player information screen.
Just enter your new player name and confirm.
UR Units & Tier List
Espers List & Tier List (Summons)
Reroll Guide: Tier List & Tips