Huxtaburger, an offshoot of restaurant Huxtable, now with four outlets and much hipster love, offers a selection of burgers named after characters in The Cosby Show – including the now unfortunately named "Bills".

Two women went public in November last year with allegations of rape against the entertainer, which in turn led many others to speak out. New York magazine put images of 35 women who had accused Cosby of raping them on its cover this month.

There are numerous examples of companies revising or editing their images after scandals break, the most memorable perhaps being Rolf Harris' conviction for sexual offences, which led to several of the murals he had painted being covered over.

But Daniel Wilson, Huxtaburger's co-owner and the man behind the name, says the menu won't be changing.

"Probably 80 per cent of our customers don't know what it means, although obviously that's not a reason not to change it.

"Obviously it's very innocent, it's based on the show. We took the names from the show, not anyone's personal life that has unfolded.

"As they say, hindsight is 20/20 but I guess you could make a comparison to Rolf Harris and what not. We unfortunately don't have a time machine to go into the future."

Who's your favourite member of the (burger) family? Bill? Theo? Sondra? Denise? We wanna know!Posted by Huxtaburger on  Wednesday, 27 August 2014

Interestingly, in a cookbook Huxtaburger put out last year, the Bills burger was renamed the Cliff Burger, Cliff being the name of Cosby's character in the show.

In an interview in 2010 Wilson said if there was one celebrity he hoped would one day visit Huxtaburger, it would be Bill Cosby.

The long-running Cosby Show starred the Huxtable family – although that wasn't the inspiration for Huxtable and Huxtaburger's names, even if it did inspire the menu.

"Everyone assumed that it came from The Cosby Show, which it does not,"  Wilson says.

"There were three business partners, and two of the three had not had a business before. I came up with the name Huxtable because I was thinking about just words and names and some kind of connection, and for two of us it was a "brave new world" – and I thought of Aldous Huxley. And I liked the Hux part, but Hux for a word is too weird for a restaurant."

The burger bar's menu features:

The Bills: named for Cosby, the Bills is a classic Aussie burger – bacon, egg, pineapple and beetroot.

"It's the one that the dad would eat," Wilson says.

The Clair: named after Bill Cosby/Dr Heathcliff Huxtable's wife, the Clair is packed with southern fried chicken, coleslaw and mayo – because Clair was the "southern" one.

The Rudy​: Huxtaburger's kid burger starring tomato sauce and mayo. Named for Rudy, the Huxtable family's youngest child.

The Theo​: All meat all the time, with a double patty, bacon and barbecue sauce. The burger the teenager of the family would eat.

The Denise: comes with jalapenos. Named for Denise – "she was the hot one",  Wilson says.