Since the phenic system is not empirical, I doubt if a scientist would use it at all.
Every known living organism on Earth is classified and named by a set of rules. Those rules are used by all scientists around the planet. The names are called scientific names, not common names. Common names are the ones you might use when talking with your friends. You call your pet a dog or a cat (the common name). Scientists call those animals by a set of several names like Canis familiarus. That's a dog.
Scientific names follow a specific set of rules. Scientists use a two-name system called a Binomial Naming System. Scientists name animals and plants using the system that describes the genus and species of the organism. The first word is the genus and the second is the species. The first word is capitalized and the second is not. A binomial name means that it's made up of two words (bi-nomial). Humans are scientifically named Homo sapiens. You may also see an abbreviation of this name as H. sapiens where the genus is only represented by the first letter.
The taxonometric way of classifying organisms is based on similarities between different organisms. A biologist named Carolus Linnaeus started this naming system. He also chose to use Latin words.
Taxonomy used to be called Systematics. That system grouped animals and plants by characteristics and relationships. Scientists looked at the characteristics (traits) that each organism had in common. They used the shared derived characteristics of organisms. Scientists were then able to find the common ancestry of the organisms. So if you had a nose, scientists would trace back all creatures that had a nose. Then they thought that you were related to them (because you all had noses). Organisms are now organized by a combination of observable traits and genetics, not one superficial trait (like a nose).
Over the years there have been different ways of grouping the living things on Earth. Some scientists have used something called a Phenetic System that uses phenotypic similarities. Phenotypic means "physical." Scientists compared what animals looked like, not their genetics. Also, organisms were grouped according to their similarities. For example, a dolphin could be more like a fish than you, because they swim and have fins. But in reality, they are mammals and have more similarities to you than to any fish.
As an aside, there is something called genotypic similarities that are genetic in nature, like the number of chromosomes you have.
Scientists also used a Cladistic System when they used phylogenic similarities. The phylogenic system uses evolutionary similarities to group organisms. So birds might be related to dinosaurs, which are reptiles, because scientists think that birds evolved from early dinosaurs.