With a three syllable name like Jennifer, I usually just shorten it to Jen when I am talking to someone else, as long as they are ok with it, I use Jen and Jennifer equally with my Jen friends. And, I have a lot of them. I have about 14 facebook friends, and the majority I really know them, not just online friends. Additionally I have other Jennifer acquaintances who are not fecbook friends. I have one friend who goes by Jenny, she introduces herself Jenny, facebook name is Jenny (her legal name is Jennifer) I met her as an adult, and it is a little odd for me for some reason to call an adult Jenny, but she is the only one of all those girls I grew up with and have met over time who uses Jenny regurlarly.
I agree with @wundayatta the thing that matters most is what the person herself prefers to be called. My real name can be shortened to a y ending and only a few people call me that. My dad on rare occasion, three male friends, who one of which says it to kind of tease me, but I think he has become used to it now, so that is my name at this point for him. And, my husband sometimes uses it. I don’t really identify as that name, so when a stranger calls me it I don’t know they are talking to me, unless they are littleraly right in front of me talking to me. But, the few people who call me it, It is endearing, it makes me smile, I like it. I would not really like it at work though or to be introduced by that name.