Private is a post given to every condidate of tranning camp who went there for get tranning.And he was knowns as peofessor because he know all the answer of question asked by tranner.That's all.

Private in Private Quelch:
Private in Private Quelch refers to the fact that Quelch was a reserved and introverted individual who preferred to keep to himself. He was not very social and often kept his thoughts and feelings to himself, hence the term "private" in his nickname.

Why was Quelch called the Professor:
Quelch was called the Professor because of his scholarly demeanor and his vast knowledge on various subjects. He was known for his intelligence, academic abilities, and his love for books. Quelch was always seen with a book in hand and was known to be well-versed in a wide range of topics, earning him the nickname "the Professor."

Quelch's serious and studious nature, as well as his habit of correcting others' mistakes and sharing his knowledge, further solidified his reputation as a scholarly figure among his peers. Despite his strict and sometimes overbearing demeanor, Quelch's intelligence and academic prowess set him apart from his classmates and earned him the title of "the Professor."