What I was trying to say is that that's not Italian. It's US English :)

But that's more of an (american) english word that vaguely looks like it has an italian origin.

They only sell bootlegs

Is that a promise?

That is english, not italian

Interestingly Wiktionary weakly supports my hunch that it was a last name.

Uncertain; said to be of Mafia origin, from the Fugazy Continental limousine company in New York City which was owned by William “Bill” Fugazy, due to its cheesy “look like a rich guy” advertisements of the 1970s and 1980s, or its alleged poor business practices,[1] possibly influenced by Sicilian fu cazzu (“it was nothing”). The word was popularized by the film Donnie Brasco (1997), based on the book Donnie Brasco: My Undercover Life in the Mafia (1987) by American former FBI agent Joseph D. Pistone (born 1939) who used the name “Donnie Brasco” as an undercover alias. First use in English appears c. 1974 in the novel Bones of Contention by Nicholas Gage. Adjective

fugazi

(US, slang) Fake. 

What people though? I've seen this 'fact' mentioned online which seems to trace back to some 2022 article. But growing up Fugazi was seemingly always considered emo.