Cubs have their own name so that when you walk into a pet shop and ask to purchase a kitten, they don't hand you an 80-pound animal that immediately bites your arm off.
The word 'cub' has been used to name the young of all sorts of wild creatures - even including the whale! - for about half a millennium. Little lions were originally specifically called 'whelps', though that is another word that came to be applied to the young of other creatures, especially dogs. As regards lions' young, they have been more or less exclusively called 'cubs' since the mid 18th century