I'm talking about the guy from the Three Kingdoms. I know he was also called Cao Mengde etc. Isn't that like calling George Washington "Washington Washington"?
Did the ancient Chinese not find it strange?
Remember that the Chinese have lots of things that look like "they're spelled the same" when transliterated from the thousands of Chinese characters to the latin alphabet, particularly when this is done without indication of the tone in Chinese. They're not at all the same when written or spoken in Chinese.
What we write as "Cao Cao" is, in Chinese, 曹操 -- two different characters, with different tones. So they're not only written differently in Chinese, they sound different too.
The first "Cao" - 曹- is a very common Chinese family name, with tone 1, often written Cáo
The second "Cao" - 操 - can mean a lot of things, some rude; can be used as here as a given name Cāo with tone 5.
So to a Chinese eye or ear, the "Caos" in 曹操 are as different as the "George" and "Washington".
[NB — these are contemporary tones, I don’t know what they were in his own time, or when the Romance of the Three Kingdoms was written, the tone structure has changed over time in many cases]