Likely a reference to Bugsy Siegel, the infamous American mobster, or the 1991 film 'Bugsy' starring Warren Beatty about his life. Frasier uses it to mock Niles's gangster affectations.
↗ Read on WikipediaMentioned once in A Word To The Wiseguy.
A Word To The Wiseguy
Season 3 · Episode 15 · S03E15
“Knock it off, Bugsy!”
From the same episode and category.
“When he wakes up you must get him to tell you about his stint as security coordinator for Jimmy Hoffa!”
“she spotted a stunning pair of Ferragamo pumps. Well, I need not remind you what effect a Ferragamo sighting can have…”
“Just think of Zsa Zsa Gabor, or Leona Helmsley.”
“Just think of Zsa Zsa Gabor, or Leona Helmsley.”