Please ask for the surname, there are several possible meanings:
1. Ask for the other party’s surname. Ancient people had names and nicknames when they reached adulthood, and people who were close and familiar called each other by nicknames. For example, Qin Zhongzhong's nickname was Jing, and Baoyu later called him Jingqing.
2. Ask the other party to give you calligraphy and calligraphy.
3. Ask the other party to name it.
The question did not provide the original chapter and paragraph, so I can only give a general answer. According to my impression, it is most likely the first one. When Baoyu first met Qin Zhong, he asked for his cousin's name in order to get intimate.