Why is the castle called a Rook?
I don't remember which language it is, but I think in one of the books I have it was at one time called a rukh, which in the book was translated as guardian. It kind of makes sense as the move of castling puts the king in a safe position with his guardian beside him. Also notice that in the Isle of Lewis chess set, it is not a tower, but a warrior. I don't know how accurate the book was, but it seems reasonable to me.

Chaturanga (India, ~1400 years ago) had Ratha (also known as Śakaṭa) and it meant chariot (wheeled transport). Rules for this piece were identical to modern rook.
Shatranj (Iran, ~700 years ago) had Rukh (also meaning "chariot"; from Persian رخ rokh). Not warrior, not guardian, but chariot.
Persian war chariots were heavily armored, carrying a driver and at least one ranged-weapon bearer, such as an archer. The sides of the chariot were built to resemble fortified stone work, giving the impression of small, mobile buildings, causing terror on the battlefield
The "rook", for most of chess history, wasn't a castle/tower like piece, that's a relatively recent development ("recent" in the context of the age of the game of chess). It only became that after a certain someone standardized chess pieces around 1850. "Tower" designs have existed before that, yes, but there were also a number of concurrent designs having nothing to do with towers/castles.
Like many others mentioned before the name comes from the middle east/India and carried on through the centuries, there's no need to rename it just because of what it looks like at the moment. In a lot of European languages however the piece is literally called "tower" (translated from Turm, toren, tĺrn, tour, torre to name a few).
The word rook evolved from persian word rukh which means chariot. This word was taken form Indian word hathi which means elephant. In olden day after the invention of chariot, usage of elephants for battle became less. Hence when persian were introduced to chess they named it rukh.
Exactly, it looks like a tower, part of castle. And it is "tower" in most languages. Castle/fortress is second by popularity. In some languages it is elephant, ship/boat, chariot, cannon.
Why elephant, here's probably why:

In a famous 11th century French chess set (which I like more than ambiguous Lewis chess set from 12th century), Rook looked like this (4-horse chariot):

Funnily, Bishop is often called elephant too, in most languages actually. And in that same 11th century set it was an elephant:

While Knight is just "horse" in most languages.
