Classes taught entirely in English still name postures in Sanskrit. The retention is practical rather than decorative.
The names are compressed descriptions
Most posture names are compounds ending in the word for seat or posture, preceded by what the shape resembles or which part of the body is involved.
The compound encodes the instruction. A name specifying a direction, a limb and a shape carries more information than a translated label usually does.
Learning the components rather than individual names lets a student parse unfamiliar postures, which is how the vocabulary is designed to work. A few dozen roots and prefixes cover most of what a class will name.
A shared vocabulary crosses languages
Yoga is taught in dozens of languages, and a common set of names lets a student follow a class where they do not speak the instructor's language.
This is the same reason other international practices retain terminology from a single source language rather than translating it locally.
Without it, every translation would fork, and a posture would acquire a different name in each market. Teachers travelling to train abroad would then have to relearn the vocabulary at each stop.
Translation breaks the system
English renderings are usually chosen for how they sound rather than for consistency, so related postures end up with unrelated English names.
The grammatical relationships between names disappear, and with them the ability to infer what an unfamiliar posture involves.
Some translations also fix on one sense of a word that carries several, which narrows the name rather than rendering it.
Continuity of instruction keeps terms fixed
Teachers largely teach as they were taught, and terminology is among the most conservative parts of any transmitted practice.
Where authority is claimed through a lineage, using the lineage's vocabulary is part of demonstrating the connection.
Changing terms would obscure that link, so the incentive runs strongly toward preservation.
Where English took over anyway
In general fitness settings, English names dominate because the priority is a room following an instruction immediately.
A handful of postures are near-universally known by English names even in traditional studios, usually the simplest shapes taught to beginners.
The split tends to fall along how a class positions itself, with Sanskrit signalling a connection to the tradition and English signalling accessibility. Many teachers use both, naming the posture once in each, which resolves the tension at the cost of a few seconds.