word choice - When is it appropriate to use "titled" vs. "entitled"?

The verbs entitle and title are synonyms. Regarding nouns, title is a noun, entitle is not. Title on its own is an adjective (the title story - the story from the book the book got its title from), entitle is not. Entitle has an additional association to the meaning of having rights to or honor: I was entitled to the deduction.

The verb entitle regards the given name as a more distinguished feature of an object, more than the verb title.

When you say

The book is titled "Far away from here".

you are saying that technically it has that title, but when you say

The book is entitled "Far away from here".

you are implying some sort of preference, either that you liked the book, or that the title was appropriate, or that the book has become famous, or that you want to suggest people to read it, something that gives to the book more than just a simple title.

I entitle this book with her name.

means I am giving this book something special by giving it a title of more importance to me, suggesting strong emotions.

The director wanted to title the movie "Loud air".

means what it says. In this sentence using entitle instead of title would be kind of strange, unless something more is said about the movie or the director.

In your sentence "I really liked..." suggests preference, honor, and, although titled and entitled are both correct, entitled suggests "appropriately titled" or "nicely titled" which is what the author really wanted to express.