What is FuBing?

No, it's not a last name, it's just a name.
No one knows what’s the meaning of “FuBing”, because it could be
anyone’s last name. And there’s no emperor in Chinese history with a last name of “FuBing”.
If you say “FuBing system”, then most people who have studied Chinese history know, somehow, little about it. As it’s the ancient military and farming system, which I think lasting for a period of time, may be hundreds years. As to the details, unless someone who study or have an interest in ancient Chinese history, no one known the detail about it.
To be a name of any kind of materials, tools, methods, foods, vegetables, systems, functions, … almost everything, in most cases, is formed from more than one word. there are few cases, which like “蛇”: means snake, it is just one word. Because for only one word, even though, it has some basic meaning, but its meaning might be obscure or broad. So, normally it’s not enough to form a noun.
Only people have surname and last name. Besides people, all the items, include animals have names, but it’s not last name, it’s just a name.
Oh, I am English learner. I am now practicing my English writing with hope you can understand.

Chinese surnames are almost never more than one syllable long. There are a few two-syllable surnames (Sima and Ouyang are a couple of the most common ones) but I don't think Fubing is one of them.

Also, note that in Chinese names, the surname comes first and the given name comes last. So, Xi Jinping is "Mr. Xi" and his friends, of which he has none because he's a filthy dictator, might call him "Jinping" or more likely "Mein Fuehrer."