salam, I am wondering if you could elaborate on a certain hadith in al Khisal: THE MIND OF A MAN BELONG TO THREE : Abu Abdullah(A.S) said: The mind of a man belongs to three; in his beard’s length; in the carving of his ring; and in his surname. I am guessing that the surname means something to do with genetics, and the beard implies having a beard is good for your mind. However, I am very confused regarding ring carvings. Could you inform me about the meaning of this hadith? Thank you very much, I appreciate it greatly.

Means these three things indicates intellect of the person as you mentioned two of them you understand but carving of ring yes what ring he wear it shoes his wisdom and carving like naqsh on ring what is written it shows his intellect and thoughts.
Like our aimmah has naqsh like
Tawakkaltu alallah