What is the rule for using "of" after generalizing nouns?
Consider these examples:
We went to the city of Rome. / We went to the city Rome.
He was born in the year of 1941. / He was born in the year 1941.
Kafka is known for the book of "The Trial". / Kafka is known for the book "The Trial".
We live on the planet of Earth. / We live on the planet Earth.
I like the fruit of apple. / I like the fruit apple.
We bathed in the river of Thames. / We bathed in the river Thames.
Where did the chemist of Linus Pauling live? / Where did the chemist Linus Pauling live?
In Africa we can find the mammal of lion. / In Africa we can find the mammal lion.
The City of Rome is correct as there is the possibility that you were visting some other region associated with Rome, such as its commune https://en.m.wikipedia.org/wiki/Rome. This would be particularly true of New York where you could visit the State of New York without going within hundreds of miles of the city. This form can be applied to all cities and towns so applies to Rome.
Either is correct but the 'of' is less frequently used. Perhaps it is a remnant of "The Year of Our Lord".
Kafka is known for his book "The Trial". The book of "The Trial" would be an account of or commentary on a famous historical incident known universally as "The Trial", or possibly a book retelling the story of a film or play called "The Trial", or possibly the story and dialogue of a musical called "The Trial".
We live on Planet Earth. The name Earth refers directly and unambiguously to the specific planet so does not require an 'of'. Unlike Rome, Earth does not have any surrounding space that we could live on.
"I like the fruit called 'apple'"; or "I like apples"; or I like the fruit of the apple tree". "Apple" is unambiguous and there are many individual apples, however all apples are the product of apple trees which can be referred to generically as "the apple tree"
We bathed in the River Thames. The name refers only to the river, not to any surrounding area. There is the valley of The Thames but this is not The Valley Thames so cannot be confused with the river in the way that a city can be confused with a state.
Where did Linus Pauling live? Pauling was a chemist, he did not posess a chemist. You could ask "Where did the father of Linus Pauling live?" since Pauling had a father.
In Africa we find the mammal called lion. Just like liking apples except there is no tree.
Basically where the object of the sentence owns the preceding term and there is potential confusion, eg Rome 'owns' the city and also 'owns' the commune, you need an 'of'. The same applies to the father of Pauling since omitting the 'of' might suggest that Pauling was a Roman Catholic priest.
In cases where the two words form a single Proper Noun (River Thames, Planet Earth) no 'of' is needed since there is no ownership.
Where the object does not 'own' the preceding term (apples do not own fruit, lions do not own mammals) no 'of' is needed, but the resulting form is not always normal usage.
In the case of authorship the book is owned entirely by the writer in the case of fiction but the subject of the book can be said to 'own' the book if the subject pre-exists.
This leaves only the year, and by extention months, as in "The month of September". Possibly this is to avoid confusion with "the early part of September" and "January of 1945". If this is the case then the periods of time can be said to 'own' their subdivisions and their full terms so an 'of' can be used.
I hope that you agree and find this answer useful