Why is diazobenzene named so and not phenyl diazobenzene?
Diazo group is $\ce{=N2}$.

Example: diazomethane $\ce{CH2=N2}$
(detailed structure: $\ce{H2C=N+=N- &lt;-&gt; H2C^{-}-N+\bond{#}N}$)

$\ce{-N=N-}$ is azo group.

Example: azomethane $\ce{CH3-N=N-CH3}$
However, preferred names are based on diazene $\ce{HN=NH}$, so better name for azomethane is dimethyldiazene.

So, note that “diazobenzene” does not exist. You obviously mean “azobenzene”, $\ce{C6H5-N=N-C6H5}$, whose preferred name is diphenyldiazene.