Did I set up my book series titles and ISBNs wrong?

Question

I currently have 4 books all under one series that are self published. The way I have been setting up the titles through Ingramspark and under my ISBNs has been:

Title: Name of the Book Series

Subtitle: Name of individual book.

I'm wondering if that is correct at all and can't seem to find any information regarding it. Take the Twilight series for example, it tells you it's a series in the actual book title. However a book series like "Left Behind" does not have the series name in the title at all, it is only in the first book, yet we know that each book is a part of that series. I'm going to use Twilight as my example because they are the closest to how I've been titling the books in my series: If I were to assign a book series like Twilight with the individual ISBNs and upload the book to Ingramspark and KDP Amazon, would it be:

Title: The Twilight Saga:

Subtitle: Eclipse

or

Title: "Eclipse"

Subtitle: (left blank)

Is there a way to assign individual ISBNs to a specific book series so that a reader who comes across your book, or say a library carrying your books, will know it is a series? I have recently come across information regarding ISSN numbers, but from what I gather, this is not for a book series, but for magazines and other recurring publications. How do you tie together all of your books so that they are recognized globally as a series? KDP Amazon has a box with the option to add your books to a series, but I've seen other self-publishing websites that do not. I have also not seen this option when assigning my ISBN numbers.

So my question is, how do you title books in a series correctly using the "Title/Subtitle", and how do you tie all of your books together through ISBNs?

I setup my ISBN numbers through Bowker if that helps.

Answer 1

What I did in my last book was this (this is an example, I didn't write this book):

Title: Name of the actual book e.g. The Chamber of Secrets
Subtitle: The series, e.g. The Harry Potter Series

I really hope this helped you. I had this exact same question, when I published my first book.

Answer 2

You first would want to name the series (example below), then following along that as a base line make the tiles of the book relate to the series' name.

Series name: Tales of the Twisted Book names: Valley of balloons, The Darkest Corner, and The Wandering

(These titles are all copyrighted)