(1) Zhu Ci continued to serve under Zhu Xicai , and it was said that because they shared the same family name , Zhu Xicai greatly trusted him .
(2) Zhu Ci continued to serve under Zhu Xicai , and it was said that because they shared the same surname , Zhu Xicai trusted him greatly .

Do these two sentences mean the same thing?

OPT:
(I). no.
(II). yes.
(II).