Cambridge and Collins are wrong! 名 just means name. It doesn't mean English first name. Is it "其名"? I embolded it in Cambridge's example sentence.
first name | translate to Mandarin Chinese: Cambridge Dictionary
the name that was given to you when you were born and that comes before your family name
名,名字
It can be rude to call people by their first name if they are much older or more important than you. 对年长或级别高的人直呼其名是不礼貌的。
Chinese Translation of “first name” | Collins English-Chinese Dictionary
first name
n (c)
- 名 (míng) (个(個), gè)
名 just means name
, sure, but 名 definitely does not mean surname, and isn't even part of the word for it (which is just 姓). By itself, 名 only refers to first name when referring to a person.