نَعَمْ، زَيْدٌ أَقَرَّ بِأَنَّ عَلَيْهِ كَذَا
Yes, Zayd admitted that this obligation was upon him.
When a witness is asked about an admission, explicitly naming the person can put the statement on record. Using the name rather than merely a pronoun serves tasjīl ʿalā al-sāmiʿ: the addressee hears the declaration stated unmistakably.
The purpose extends beyond identification: it makes evasive denial of the explicit statement harder. The evidentiary setting, the question, and the answer determine the rhetorical role.