Written accounts of Welsh rabbit appear as early as 1725, but the name Welsh rarebit first appears later, around 1785. This simple but very popular dish of toasted bread covered in melted cheese and topped with mustard or spices has been popular since at least the 1500s under the name of caws pobi, which is Welsh for toasted cheese.
Most historians agree that the name Welsh rabbit caught on as a joke, but their interpretations differ. In the late 17th and early 18th centuries, the English often gave laughably fancy names to any food or product common to a region or profession. For example, they called red herring Billingsgate pheasant, and cow heel became cobbler's lobster.
The English also used the adjective Welsh to describe an item of inferior quality. A Welsh pearl, for instance, might have a low grade or even be counterfeit, and using a Welsh comb meant brushing your hair with your fingers. By this reasoning, Welsh rabbit is an inferior form of rabbit or a main dish for people who can't put real meat on the table.
As the dish gained in popularity, the name rarebit became more common. The name change was probably an attempt to make the name more fitting to the dish and drop some patronizing overtones, according to the Oxford Dictionary.