A 'phylogeny' displays classification as trees. Why is this name appropriate?

Due to it's root word, Phylum.

Explanation:

Phylum's textbook definition reads - a principal taxonomic category that ranks above class and below kingdom. Phylogeny is the study of Phylogenesis, which to a broad degree, is the classification of organisms.

P. S. Phylogenesis also discusses the evolutionary process of said organisms.