You can name your fish when you purchase them: 1. Tap the text in the Name field. 2. Generate a random name in the pop-up window and tap OK to confirm. You can also generate random names for the fish you buy by tapping the icon with the two arrows next to the Name field.
You can also change names whenever you want: 1. Tap a fish to open the menu below. 2. Tap the pencil icon. 3. Pick a new name and confirm by tapping OK.