From my personal observations from living in Taiwan for years, I found that it really varies, depends on what people are used to in that particular town or area, depends on the level of formality or familiarity, the person's who is calling the name personality and what the named person introduces themselves as.
Calling each other by full 3-character name seems common in some circles even among close friends (my girlfriend often even calls her parents and brother by full name casually, and most of her friends from school exclusively by full name in an affectionate way), completely nonexistent in other circles and in others yet only certain people are called by the full 3 characters, while others are not.
Using the 2-character given name seems to me to be the most common form of address between informal casual acquaintances, ,schoolmates, university students, members of a club, etc., where everyone is roughly of same age or rank and nobody is long-term friends with anyone.
In groups with long-standing relationships I would say most people have a nickname and expect to be addressed by it over their name. Sometimes, especially down south, the nickname is a character of their name prefixed with 阿, such as Awei, Ajie, Ajou, Amin, etc. Sometimes it would be 阿+another random name or word that is unrelated to their real name. The above also applies to using 小 instead of 阿. 小 is often also used with just their surname. Other nicknames seem to be completely random words that people are called (and call themselves) that translate to things like cucumber, chicken, bucket head, whatever. Totally random.
English names are also quite common as nicknames that they are know by over their real names. This is in my experience more common up north, in metropolitan areas and groups where people tend to speak more English, especially the entertainment industry where colleagues wouldn't even know the Chinese name of someone who calls themselves by an English name. Something like 大家好我是Cindy is very common to hear as an introduction, even on the radio.
Edit: Forgot to include another very common nickname type which is used pretty much exclusively by girls: reduplication. Taking one character of their name and doubling it, making that their nickname. Like NingNing, TianTian, JiaJia, HuaHua, etc.