You are an ecologist who discovers a new species of algae living in the fur of the brown-throated sloth. whose system of naming will you use to classify this new organism?

You will use the Linée Classification System

Explanation:

Linée, the naturalist, physician and teacher, created a system of classification and nomenclature of living things in 1735, which is still used today with few modifications.

In Linée's system, all living things are grouped into different categories. In all there are seven taxonomic categories. The largest and most comprehensive is the kingdom. Each kingdom is divided into phyla. Each phylum is subdivided into classes. Each class is subdivided into orders. Each order is subdivided into families. Each family is subdivided into gender. Each genus is subdivided into species.

The species is the basic category. In it are individuals who are capable of reproducing among themselves and of producing fertile descendants.

Thus, the Linée Classification and Naming System is the best system for an ecologist to correctly classify and name that algae.

You would most likely be using Carl Linnaeus' form of naming species known as

Binomial nomanclature ("two-term naming system")

It's how species get names like

"Homo sapiens" (Humans)