According to this Telegraph article Molly was also the most common name for both cats and dogs last year (Sadly Tiddles doesn’t get a look in)
So if a house has a pet called Molly does that make it a Molly House?

A Molly House is an 18th Century term for a meeting house/brothel for gay men. One of the most famous, or perhaps notorious, of which was run by Margaret (aka Mother)Clap in Holborn. In 1726 the local constabulary raided the house and Mother Clap was sentenced to the stocks. It is believed that she died of the injuries sustained during this time – being sentenced to the stocks was often a lingering death sentence - three of her patrons were hanged at Tyburn.
Or perhaps it just makes a house with a cat or dog called Molly, Perhaps having four cats makes this a cat house…
Interestingly Mother Clap does not seem to have given rise to the slang term for gonorrhoea though; that is believed to come from “clapier”, the Old French word for brothel.