Import from RSS missing blog post author names

Brand new to WP, and am trying to migrate a big site that was done in a custom CMS. So I wrote a script to put the old 4000+ post blog into an RSS file that matches the syntax of the WP rss feed. Then I segmented it to make the import files small enough to be accepted.

My problem is that none of the blog post author names are being imported. I’m guessing the authors need to be set up as WP users before the import, but I’ve tried that with one or two of them, and all posts still import under the same author name (the name of the site).

Is there a trick to make this import correctly?

Thanks.