غُلَامُ زَيْدٍ — Zayd’s servant.
غُلَامُ: first term of iḍāfah, declined according to its sentence role.
زَيْدٍ: genitive second term with kasrah.
بَعْلَبَكُّ — a compound proper name.
بَعْلَ: first component built on fatḥ.
بَكُّ: second component nominative as a diptote.
Both look multi-part, but one is a genitive construction, while the other is a single compound proper name.