We used to call them 'blow-offs' when I was a child. This was from school as I can't remember using a word for it at home, it was just dirty looks and laughing about it.
There was a rhyme at school: 'show-off, show-off, pick your nose and blow-off'.
I say fart now but dd says 'bottom burp' which I had never heard before but which I think comes from her nursery.
An acquaintance who is quite strict and has a dd who is treated like a princess told this story. Her dd came home one day whispered: 'Mummy, I know what the F-word means.' Her Mum was perturbed and not happy that her dd knew the 'fark' word already. You guessed it - the 'F-word' was 'fart'. How awful!