Is there another name for unrendered lard?
As the Wiki says, unrendered lard is "adipose tissue", also called "fatty tissue". It's often referred to by the specific piece of fatty tissue that it comes from: fatback, belly fat, leaf (from around the kidneys, the equivalent of beef suet). 

It can also simply be called "fat". I see, for example, many articles to render fat into lard. That's more ambiguous than "fatty tissue", but it's much more colloquial and it's usually clear from context.