أَبُو حَفْصٍ is a kunyah. Adding عُمَرُ clarifies which person is intended.
If the second word instead described a property, such as «الْعَالِمُ» (“the learned”), it would ordinarily function as naʿt, not this identifying use of ʿaṭf al-bayān.
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From kunyah to personal name
ʿAṭf al-Bayān: Definition, Examples, and Contrast with Badal
أَبُو حَفْصٍ is a kunyah. Adding عُمَرُ clarifies which person is intended.
If the second word instead described a property, such as «الْعَالِمُ» (“the learned”), it would ordinarily function as naʿt, not this identifying use of ʿaṭf al-bayān.