姓氏 refers to surname, and 名字 refers to personal name.
But I’ve heard people using the separate characters to talk about surnames and personal names.
For example:
我的中文老师姓姚
林氏集团 (Lin’s Corporation, like one of those companies named after their founder)
她名叫小丽
字: I’m not too sure about this one, but I know 李白’s 字 is 太白
What is the difference between all these?
From my answer to this question What does this symbol mean? I explained 姓氏 It may be a good reference to your question
From my answer to this question Why is there such a difference between "first name" and "last name"? I explained 姓 and 名字
In the past, most people in high society would have a 姓(family name), a 名 (given name) and a 字 (Courtesy name)
Example of using individual characters in 姓氏 and 名字:
他姓曹 = his last name is 曹
曹氏一族 = the clan of 曹 family
他姓曹，名操，字孟德 = his last name is 曹, first name is 操 and his courtesy name is 孟德
