WordPress.com inquiries DO need to go to the WordPress.com's own Support page HERE, but I can at least partially answer your question (I think) because of the overlap of self-installed WPs and WP-hosted WP installs.
In short, unless you have a theme from WordPress.com's theme collection that specifically removes the dates and names, you will need to be able to get into the theme's templates themselves to remove the coding that propagates that information for you. Thing is, WordPress.com offers CSS customization, but I am not sure if they allow complete theme customization.
That said, my advice would be to head over to the WordPress.com support forum and ask around if there are any recommendations for a theme that purposely removes the author and posting date information from being displayed in addition to any other theme requirements you may need.
Best of luck!