Did some people only have names like 张三?
Were some people in the past actually known just by names like 张三?

Yes. It is the official name of some people, not just one. Some female even names as 张三妹. Bu the way 刘三姐 is a very famous movie.

张三, 李四, etc. are not nicknames, they are real names, they are also used as a "any one" placeholder, as in the answer of other question. For example, 你到那儿去，认识谁是张三，谁是李四啊. Going to that far, you do not know whom to contact.

Add more: (How are those names now?)

My father has a very close relative who is 李四 officially. He would be 80 or 90 now. 

On my mom side, there are two brothers having names 大水, 二水. The man 大水 was born the year of a huge flood. It is smart to use 大 for big/huge and also for the first son. In Chinese 老大 means the eldest son. 

Ha, you will see, 老大 is the head of an criminal gang. Haha, again, you understand the joke, Xi DaDa. 

By the way, check out sons of 赵紫阳, from 赵大军 to 赵五军, (at least five).