What is the name of the traditions that focused on the worship of specific deities such as Shiva, Vishnu, and his avatars (incarnations) and forms of the goddess or Devi, all often conceptualized in anthropomorphic forms called? 

Saguna

The historians of religion often classify bhakti traditions into two broad categories: saguna (with attributes) and nirguna (without attributes). The former included traditions that focused on the worship of specific deities such as Shiva, Vishnu, and his avatars (incarnations) and forms of the goddess or Devi, all often conceptualized in anthropomorphic forms.