You don’t need an ISBN number to sell a book on Amazon. Many books that have done extremely well on Amazon have done so without an ISBN.
If you are reading this I would assume you would know what an ISBN number is, but if you don’t, it’s a unique number that identifies a book. Each edition of a book has a different number, and each format of a book has a different number. All of the mass market paperbacks of the first edition of a book will have the same number, but the hardcover and the mass market paperback will have different numbers. E-books should also have unique numbers.
In the US ISBN numbers cost a bit. I believe somewhere in the range of $125.00 per. The more you purchase the less each number costs. Amazon will let you use an ISBN for free, which lists them as the publisher. Nothing wrong with it.
Here in Canada we have more options. In fact, if you establish a small publisher you can get as many ISBN numbers as you want, for free. ISBN numbers are unique worldwide. If you search for a book by ISBN you will find that particular title and no other.
I started selling books before I had my own ISBN, so I started with Amazon generated numbers. Now I have my own numbers, and I will be re-releasing all of my books with my own ISBN’s that list BrightCrow Publishing as the publisher.