What are young panthers called?

Panther is a generic term and does not apply to a single species. It may refer to
a lion - panthera leo - Africa and Asia
a tiger - panthera tigris - Asia
a leopard - panthera pardus - Africa and Asia
a jaguar - panthera onca - South and Central America
a snow leopard - panthera uncia - Asia

The young of all species are called cubs.
Panther babies are called kittens. There are usually 1 to 4 in a litter. They normally stay with their mother for about 2 years, before leaving to find territory of their own. For more details, see the sites listed below.

They are also called cubs.