I have no idea of what kind of themes are able to create a site where sellers can registrate themselves and sell their own products. Is there a name for it? How do I search? Do you have any suggestion of a great template? Please help!
Look for multivendor marketplace.
One of my all time favourite themes is:
And another example:
Though it isn’t always easy to find it…
e.g.
Wilcity can be found under
Home > Files > WordPress > Corporate > Directory & Listings
and
Martfury can be found under
Home > Files > WordPress > eCommerce > WooCommerce
Other great resources for multivendor market concept:
Dokan, WC Vendors, WC Marketplace, WCFM Marketplace, WCFM – Frontend Manager…
(some of) these plugins are often used (budled or compatible) with multivendor WordPress themes.
I hope you won’t get lost in all these really great themes and plugins and features 
Carefully check theme description page of the themes when choosing one for your project. It is always clearly stated in case a theme is multivendor ready and check demos as well and you can always ask your presales questions on the item comments page and author will answer you: how to contact the author of an item