My daughter has begun her aquarist hobby early, and has a 6.6 gallon freshwater tank in her room. It's a pretty fascinating little colony both in that her fish have a lot of personality, and that they're comfortable and happy in such a girly aquarium with brightly colored stones and neon glass starfish and shells.
The "star" of her colony is Candy, who is a male Siamese betta (Betta Splendens). He looks a little like this:
Candy is a very personable little guy and swims up to the top of the tank to say hi. Or he's always hungry and is constantly begging for food. It's hard to tell with fish.
We had purchased a dozen neon tetra (Paracheirodon innesi) that she named collectively Cookie or the Cookies. We still have about 9 living in the tank. They suffered some as we learned that the tank must only be fed once a day or else tetra eat too much and die.
The community seemed pretty happy at that point. We figured we're about at the end of the bioload for such a small environment. However, a couple of weeks led to growth of lush green algae on the rocks at the bottom of the tank and along the sides of the glass. We purchased a couple of snails, but sadly, they perished quickly without making a dent in the algae. About 2 weeks ago, my husband and daughter returned from the fish store with 2 Chinese algae eaters (Gyrinocheilos aymonieri). After a couple of days, our daughter named them Vanilla and Chocolate.
The tank is now as pristine as the day my husband set it up. Vanilla and Chocolate made short work of clearing the algae problem. They like to hang out in the little cave together, and spend most of their time eating algae off of stuff while hanging upside down.
We didn't offer any encouragement for the pet naming. We've had a 20 gallon saltwater tank in our living room since we moved in here about 18 months ago with 2 mated black percula clownfish (Amphiprion polymnus).
My husband and I rarely named our fish. But once our daughter turned 3 and everything had to have a name, she started calling them Marlin and Coral after Nemo's parents in Finding Nemo. We expected that the freshwater tank inhabitants would also receive character names, but it has been oddly themed after dessert.