Simply Guest Author Name Faq

As per Jetpack Support:

While Jetpack synchronizes some of the data associated to your site when you connect it to WordPress.com, we don't synchronize everything. In some cases, we extrapolate and build elements on WordPress.com based on some of the synchronized information. That's the case with the author links.

While this is enough for most people, it's obviously not practical for your use-case.

You'll be happy to hear that we're currently working on refactoring the way Jetpack Sync works. We want it to be more reliable, to happen more often, and to include more information so we can keep developing more features relying on the synced data on WordPress.com or in the desktop apps.

Unfortunately, I don't have an ETA on this at this point. I'm afraid I can only recommend that you keep an eye on the changelog in future Jetpack updates.

The author image in WordPress is based on a gravatar, a universal image that is associated with your email address. Ask the author for their gravatar email address. This address is usually the same address that they use to log into WordPress.com (but not necessarily).  Enter that in the section where it says Gravatar Email on the post.