Well, it doesn't solve the problem of communicating whether you are using the family name or given name, which is an important piece of information to know since it indicates the level of familiarity / intimacy / distance. This distinction is a bit less common for personal conversations in English-speaking countries but important in many parts of the world.

Perhaps I would be talking to "Cheng", but later I would be talking about "Professor Cheng".

> Perhaps I would be talking to "Cheng"

In my experience, while it is common for a Chinese personal name to be one syllable, it's not at all common for a person to be addressed by that one-syllable name. There are several strategies:

1. A person with a one-syllable name might be addressed by their whole name. For example, a 孙艺 might be called 孙艺 in speech, even though 孙 is the family name.

2. The person might have a nickname. For example, I know someone who goes by his nickname 哈哈; I've never heard his actual name.

3. The one-syllable name might be reduplicated; 袁璐 might be addressed as 璐璐.

4. The one-syllable name might be prefixed with 小; 李宁 might be addressed as 小宁.

Options 3 and 4 are diminutive constructions and may be too intimate for a strange man (or even a familiar man) to use to a woman.

I was thinking of the context where you are talking to someone in English, but they have a Chinese name. In Chinese I assume it would be much less ambiguous how to address someone with a Chinese name.

Interestingly, in Chinese no-one would call him just 'Cheng'.

And in Chinese nobody would be confused about whether his family name was Xu or Cheng.

Also reasonable:

"I am Doctor Xu."

"I'm Xu Cheng. I prefer my students to call me Doctor Xu."

"Hi, everybody calls me Frazz. Here's my card if you need to reach me."