Final answer:
The phage DNA incorporated into the bacterial genome during the lysogenic cycle is called a prophage, associated with temperate phages.
Step-by-step explanation:
The DNA of a phage that is latently incorporated into the bacterial host genome is termed a prophage. This occurs during the lysogenic cycle, where the phage genome integrates with the bacterial chromosome without destroying the host.
The process is characteristic of temperate phages which can remain latent within the bacterial cells, being replicated and passed on as the bacteria reproduce. Environmental factors may cause the prophage to become active, excising from the host genome and entering the lytic cycle, where it replicates and causes lysis of the host cell.