A private investigator.
My name is Dexter Baxendale.
Not everyone in my profession sports
a broken nose and dirty fingernails, my pubescent friend.
When Society seeks confidential assistance,
they do not necessarily hire Mike Hammer.
'MURDER, SHE WROTE'
This conversation took place in late summer, 1984, at the estate of "Captain" Caleb McCallum in New Holvang, New York. Based on standard practices here at Toobworld Central, without any accreditation to the name, we accept that Baxendale was speaking of Mike Hammer as a real person.
Mike Hammer is a Multi-dimensional. He began "life" in the 1947 paperback "I, The Jury" by Mickey Spillane and in a dozen other novels and four short stories. (There are at least nine more novels mostly written by Max Allen Collins but Spillane gets top billing in the byline.)
From there he moved on to five feature films and five TV movies, with four TV series and one unsold pilot for another show. (Coincidentally, that pilot, directed by Blake Edwards, starred Brian Keith as Hammer. Keith was one of the major guest stars in the 'Murder, She Wrote' pilot from which the above quote comes.)
Hammer also appeared in comic books eventually which had been the forum in which former comic book writer Spillane originally planned to use for his hard-boiled detective (athough his name would have been Mike Danger.)
And in the aural universe, there was a radio series as well as audio-books about Hammer.
Hammer's heyday for Earth Prime-Time (but not the greater TV Universe) was in the 1950s. But he was still alive by 1984 and his fame was probably heightened thanks to movies and books. (He's the type of character whose source material would be referenced in TV shows, not just the character himself, as seen here. In fact, his fame would secure in the future, as Constable Odo and Chief Miles O'Brien both were fans of the novels about him.) So when Baxendale cited him, he assumed Giles and the others would know who Mike Hammer was.
Someday Mike Hammer will be inducted into the TV Crossover Hall of Fame as a Multi-dimensional. He may have been portrayed by Darren McGavin originally, but it will be Stacy Keach whose visage will grace the official portrait. (Keach appeared in three different incarnations of a 'Mike Hammer' TV series as well as a handful of TV movies.)
McGavin died in 2006 and so I think we should consider Mike Hammer to have died around that time as well. In the Land O' Remakes, Hammer is still alive, although getting pretty old. But he will be immortal in BookWorld with each new reader of those books by Mickey Spillane.