Why is the inverted index called so and not simply index? In my notes is represented like this:

From wikipedia:

In computer science, an inverted index (also referred to as a postings
file or inverted file) is a database index storing a mapping from
content, such as words or numbers, to its locations in a table, or in
a document or a set of documents.

Where is the inversion with respect to a normal index (like the one found at the end of books)?

Index: (in a book or set of books) an alphabetical list of names,
subjects, etc. with reference to the pages on which they are
mentioned.

Am I missing something? Like a nuance of the meaning of the name due to the fact that english is not my main language.
Here is an array:

A[0] = Alice
A[1] = Bob
A[2] = Charlie

Here 0,1,2 are indices.
Now suppose that we want to know which index contains a given word. Then we use a dictionary:

D[Alice] = 0
D[Bob] = 1
D[Charlie] = 2

This is an inverted index (according to your Wikipedia quote).

The word index has different meaning in different contexts:

Technical books often have an index of terms at the end.
The Catholic church held an index of forbidden books.
In economics, there are financial indices.
In computer science, an index is usually an integer used to index into an array.