What is a person called when they are obsessed with correct English?

There isn't a single, universally accepted term for someone obsessed with correct English. However, here are some options depending on the specific nuance you want to convey:

Formal/Neutral:

* Grammar enthusiast

* Language purist

* Prescriptivist (this term is more specific, as it refers to the belief that language should be used in a specific, "correct" way)

Informal/Humorous:

* Grammar Nazi (this term is often used jokingly but can be seen as offensive by some)

* Word nerd

* Language pedant

* Grammar stickler

* Language snob

More descriptive:

* Someone who is highly attentive to grammar and usage

* Someone who cares deeply about the nuances of language

* Someone who is very critical of grammatical errors

The best term to use will depend on the context and your intended audience.