The scientific name for a clown fish is a amphiprioninae.

If you are asking about the "Nemo" type clownfish then they are one of the "Anemone fish" in the family Pomacentridae subfamily Amphiprioninae.

Clownfish are also known as anemonefish because they live in anemones. They are from the subfamily Amphiprioninae in the family Pomacentridae

If by domain you mean scientific name it is

Kingdom: Animalia

Phylum: Chordata

Class: Actinopterygii

Order: Perciformes

Family: Pomacentridae

Subfamily: Amphiprioninae

Genus: Amphiprion

Genus: Premnas

Clownfish, also called anemone fish, are a type of Amphiprioninae, of the family Pomacentridae. They are not included on any list of kosher or non-kosher fish. Because they have fins and ctenoid scales, they are presumablykosher. However, this answer should not be taken as a certification of kosher-status: a more knowledgeable source should be sought.