We use nicknames sometimes, for example
Kati for
Katharina etc., but it's not as common as in English-speaking countries.
My name is
Christina and there are few people who call me
Chrissy or
Chris. Only my best friends tend to use
Chrissy.
Normally, people don't come up with a nickname very quickly, but use your normal name unless you suggest they should call you by a certain nickname.
Adults are normally called by their full fn.