The appositive need not be a proper name. The second expression may be a common noun clarifying the reference of the first, so proper-name status is not a universal condition.
وَالْمُؤْمِنُ الْعَائِذَاتِ الطَّيْرَ يَمْسَحُهَا
And the one who grants safety strokes the birds seeking refuge.
In this poetic example «الطير» explains «العائذات»: the beings seeking refuge are birds. The two expressions point to the same referents; the construction is not simply a coordination of two separate groups.
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ʿAṭf al-Bayān, Badal and Coordination: Clarifying, Reinforcing and Specifying the Subject
The appositive need not be a proper name. The second expression may be a common noun clarifying the reference of the first, so proper-name status is not a universal condition.
وَالْمُؤْمِنُ الْعَائِذَاتِ الطَّيْرَ يَمْسَحُهَا
And the one who grants safety strokes the birds seeking refuge.
In this poetic example «الطير» explains «العائذات»: the beings seeking refuge are birds. The two expressions point to the same referents; the construction is not simply a coordination of two separate groups.