You should be able to do this by adding the vendor to your product page within the theme editor. (Admin > Online Store > Themes > Customize > Select ‘Homepage’ dropdown and change to ‘Product Page’).
I’ve created a video to show you how to add the vendor to the product page. If there is anything else I can help you with, please let me know.
Sorry to get back to you late. It’s possible the theme doesn’t support it on the homepage, however it’s possible there is also a setting to turn on the ‘vendor name’ like I showed in my screen recording. Except instead of changing the ‘Homepage’ in the dropdown to ‘Product Pages’ you would keep it on the ‘Homepage’ tab. From there you can see if there is a similar setting available.
If there is anything else I can help you with, please let me know.