What is the exact word (not necessarily a single noun) to use for a person who seems to be introvert when in real-life, but is very much extroverted and free when they talk to you online?
Urban Dictionary suggests netrovert.
Wikipedia goes with the Online disinhibitation effect, so a person exhibiting this behavior would be "online-disinhibited".
Well, I said if someone upvoted my comment, I would put it as an answer.
I would go with "A sheep in wolf's e-clothing", transforming the well-known idiom to indicate a naturally timid and introvert person (the sheep) transforming itself in an aggresive and extrovert person (the wolf), once it is online (the e-clothing).
As per your request, I am re-submitting my comment as an answer.
Internet tough guy.
This is certainly a very popular term, though I still maintain that it is not a perfect fit for your description. Synonyms include "keyboard warrior" and "online tough guy". Here are links to definitions from various (dubious) places:
This comic addresses the concept of your question. You could use that term.