Is there such a thing as palliative care for younger people?

Yes: Any age can get palliative care.

Absolutely!!: Palliative care can be appropriate for any age--because serious illness can occur at any age. It's not only for old people! admittedly palliative care is often part of geriatrics at many medical centers, maybe that's why you're asking? And there is not a different name for young people--even the best pediatrics centers have palliative care.