Iḍāfa compound: one noun is annexed to another, as in ʿAbd Allāh.
Blended (mazjī) compound: two elements merge into one proper name, as in Baʿlabakk.
Predicative (isnādī) compound: an entire clause becomes a name, as in Shāba Qarnāhā.
The compound cause of diptote status under discussion here applies to a mazjī proper name, not to the other two kinds.