When do people use a one-character given name alone?
You can duplicate that character (if you are really familiar to him/her). Even you can do that the same with three-char names. For example, 曾國藩, you can just call her 藩藩. You can find it if one's name have a char that pronounces the 1st, 2nd or 4nd tone, you can do duplication. For example, 张扬: 扬扬.

Note 1: Some pronunciation should be changed, otherwise it will be weird for locals:

2nd tone: The second char should pronounce as the 4th tone.

3rd tone: Won't be used in general.

4th tone: The second char should pronounce as a lower tone than the first one.

Note 2: Some Pinyin combination won't be used to duplicate.

3rd tone: Won't be used in general.

Note 3: Never be confused with the meaning of the duplicated word, you will never write them onto the formal papers right? or, you can find for some char with positive meanings to replace them.

Maybe you should ask to your friends first, they may be interested in it, LOL.