Mario and Luigi are called the Mario brothers. Does that mean Mario's first and last name is Mario, or does he have another first/last name?
From the Wikipedia article:
Nintendo did not initially reveal Mario's full name. In a 1989 interview it was stated not to be "Mario Mario" despite the implication of the Mario Bros. series' title.
The first notable use of "Mario Mario" was in the 1993 live-action film adaptation. This was again used in two of Prima's official stategy guides, in 2000 for Mario Party 2 and in 2003 for Mario and Luigi: Superstar Saga.
In 2012 after Charles Martinet voiced Mario declaring himself "Mario Mario" at the San Diego Comic-Con the next month Satoru Iwata said he had no last name, which Shigeru Miyamoto agreed with the month after. Two months after Iwata's death in July 2015, Miyamoto changed his stance September 2015 at the Super Mario Bros. 30th Anniversary festival, confirming that his name was indeed Mario Mario.
So, TL;DR, the most recent decision is that his first name is Mario and his last name is Mario.
Mario's creator, Shigeru Miyamoto answered this in an interview with GameInformer a while back.
To him, Mario and Luigi don't have last names, but in the film version, Mario and Luigi have the last name of "Mario".
“This is an old story, but Hollywood did a film version of the Mario Bros. many years back. There was a scene in the script where they needed a last name for the characters. Somebody suggested that, because they were the Mario Bros., their last name should be Mario. So, they made him “Mario Mario.” I heard this and laughed rather loudly. Of course, this was ultimately included in the film. Based on the film, that’s [how] their names ended up. But, just like Mickey Mouse doesn’t really have a last name, Mario is really just Mario and Luigi is really just Luigi.”
In 2015, Miyamoto reportedly confirmed that the brothers' last name is officially "Mario", but I have been unable to find a reliable translated source. Most news sources cite this article about the press conference; this is the translation courtesy of ixrec.
The official Nintendo name for him has been confirmed to be "Mario Mario"!
Mr Miyamoto came up on stage and stated that "Mario Mario is his real name"!
(note this might be a paraphrase rather than Miyamoto's exact words)
The character doesn't have a surname, however he was named after Mario Segale who owned one of Nintendo's first warehouse/distribution centres in America. So if you had to give him a surname then maybe Segale would be an option
One source is linked below, a piece published in the Seattle Times which states that he is a property owner and used to own the warehouse that Nintendo used, and describes that he may have been the inspiration behind Mario being named: Powerful Segale family has massive vision for Tukwila expanse.