He is called as Aquarist, Fish Keeper, Aquarium hobbyist or Aquarium or fish enthusiast.  A feminine form is not common.

Ichthyologist (someone who studies fish) would actually be the perfect answer. To do well with aquaristics, you would have to study the fish and learn what works well to keep them optimally.

Incidentally, in the Star Trek film, the Aquarians are a group of people. They live in the sea and resemble our sea cows. They communicate via echolocation. Sound can travel five times faster underwater than in the air. Whales and dolphins, among others, use this type of communication.