With only 10,000 cases per year in the entire US, probablly most dentists never even see any patients with
HPV related throat cancer; and screening and early diagnosis have never been shown to make any difference in prevention of rare cancers, only the common ones (e.g. colon, breast, cervix). But for now CDC and virtually all other such agencies and experts recommend against informing partners. We'll see what evolves over the next few years, however.