Not staff, so this isn't an official answer, but just mentioning your pen name in the establishing email at the start of the contest would be our recommendation. That way staff knows and they can follow up with it later.
You really shouldn't include your pen name on your "cover" because right now the platform does not offer covers for free series. Your "cover" is instead a 300 x 300 px thumbnail and since that is highly important real estate our recommendation would be to focus on using it for imagery only and not trying to squeeze a name in there too. It would make things too congested. That postage stamp sized thumbnail is your "billboard" in a sea of others and you want to stand out with imagery that grabs a reader by the tonsils and yanks them in head first.
On the app, the covers you see are for paid series. That is how Tapas makes it easy for readers to tell what is paid and what is free. If you get a publishing contract your postage stamp is going to nearly double in size and then you can certainly include your pen name. You probably will also want to get a new account under your pen name as well, to reduce confusion for readers, when it is time to cross that bridge.