Slippery Nipple

Hi,
Please, what article would you place before the cocktail in this sentence:

The barman did not know what goes into _ Slippery Nipple.

Thanks.

That was a frightening title.

It would depend. Definite: the, indefinite: a.

It was from a grammar test, no more context. So either is OK? The key says "a", but I doubt.

And I've been told all my life that this was a "Buttery nipple"!

A would be what I would use. You don't go around asking for ingredients for "the" martini or "the" Long Island iced tea, right?

And any bartender who doesn't know right off the bat how to make a slippery nipple should be out on his ass in the street, pronto!

I had doubts because I thought a generic name should have "the".
OK, and if we take
_Slippery nipple is not among my favourites,

then, what article?

You would use "the" in that sentence.