Mario and Luigi's last name varies depending on the source.
The name "Mario Bros." has led fans to believe that both brothers have the last name "Mario". Because of this, the 1993 Super Mario Bros. movie has its characters state their names as "Mario Mario" and "Luigi Mario". The last name appears in other sources, such as the Mario Party 2 Prima Games guide, and in the response given by the Mario Bros.' voice actor, Charles Martinet.
Other Nintendo employees and representatives, including franchise creator Shigeru Miyamoto, have formerly insisted that Mario and Luigi have no last name.
Miyamoto changed his mind at some point prior to the Super Mario Bros. 30th Anniversary festival. During this 2015 event, he stated that Mario and Luigi both have the last name "Mario".
Unlike the conflicting information regarding Larry Koopa's namesake, this represents a shift in the current internal canon of the franchise, as opposed to an altered retelling of a real-life story. Therefore, the official answer can change in cases such as these.