زَيْدٌ and عُمَرُ are both proper names.
زَيْدٌ، زَيْدًا، بِزَيْدٍ: Zayd is fully declinable and may take regular case vowels with tanwīn.
عُمَرُ، عُمَرَ، بِعُمَرَ: ʿUmar is a diptote, normally without tanwīn and with fatḥa in the genitive when neither al- nor iḍāfa changes that rule.
Proper-name status alone does not determine the difference: the other effective cause matters.
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Causes of Diptote Status — ʿAdl and Waṣf
زَيْدٌ and عُمَرُ are both proper names.
زَيْدٌ، زَيْدًا، بِزَيْدٍ: Zayd is fully declinable and may take regular case vowels with tanwīn.
عُمَرُ، عُمَرَ، بِعُمَرَ: ʿUmar is a diptote, normally without tanwīn and with fatḥa in the genitive when neither al- nor iḍāfa changes that rule.
Proper-name status alone does not determine the difference: the other effective cause matters.