By default that is how Calibre sort names. Since it does not, I assume that you have a case of bad metadata.
For the sort to function you have to make sure that the names are correct. When you add books the names often gets wrong, because the data in the book is badly formed, or you didn't do the import correctly. You can add books in many different ways, and unless you are careful the metadata will be wrong and have to be fixed.
Edit metadata for each book and make sure that the field for authors has the form first name last name (FN LN) like this:
Authors: Jane Austen
And make sure that the field for sorting, author_sort has the form LN, FN like this:
Author sort: Austen, Jane
In the Quality Check plugin there is a tool that allows you to quickly fix a lok of books that by mistake have authors in the form LN, FN.
By default Calibre displays authors (FN LN) but sorts using author_sort (LN, FN), just like a real library.
When you add books or change metadata you should always verify that both authors and author_sort are correct. Then the sort will work fine.
You can also search for "," in the authors field to find books that likely have bad metadata. Multiple authors should be separated with an ampersand (&).
It is boring to fix bad metadata, but it doesn't fix itself... Calibre still isn't smart enough to automatically fix bad metadata. A lot of the functions in Calibre are there to make it easier to get the metadata right, but you have to use them.
More information here: