A child doesnt have the same frame of reference when reading it so wont question that it has to be something else other than a cocktail.
Really depends on the child. A lot of slightly older, more inquisitive children will ask what it is and then, on being told that it's a cocktail, will ask why it's called that. If it's something like a White Russian, you can say that it contains vodka, which is the a very popular drink in/from Russia (OK, not right at the moment) or a Manhattan, you tell them that's where it originated/was inspired by. Not quite so easy with a porn star martini.
As PP said, spotted dick was never deliberately called that to be rude - 'dick' is just an old dialect word meaning doughy pudding. Cocktails, otoh, are deliberately named rude things - for no other reason than to see how far the original namers can get away with it - with the (ironically) childish deniability built in that 'it's not rude - it's just a cocktail'.
Yes, they're adult drinks, but frequently sold/advertised in places where children go. Would you be happy for them to advertise 'sex on the beach' or 'long comfortable screw against the wall'? It's probably only a matter of time before some 'hilarious' boundary-pushing person comes up with one called 'take me up the arse outside Tesco' or similar - which isn't really that different from long comfortable screw. Would that be OK?
They need to know their audience and sell them as 'passion fruit martinis' - even 'PS Martinis' if they really must. Pathetic adult jokes have no place in an establishment that actively targets families.