Kim is short for Kimberly, so I primarily go by a nickname, but it doesn't
feel like a nickname. I tried to get people to call me Kimberly for a while when I was in elementary school and Different Strokes was popular, but it didn't take. I did have one co-worker ages ago who called me Kimberly, and one teacher in high school who called me Kimmy.
At my current job I would sometimes get called Jill. The actual Jill started at about the same time, and we often worked parallel positions, so it was just a mental interchangeability for one of my supervisors. (Jill would get called Kim as well.) Jill has since moved on to a full time job elsewhere, but I still get called Jill from time to time as sort of an inside joke.
DS is Matthew and we have always called him by the full name, but a lot of his friends call him Matt. It still sounds wrong to me every time.
DD is Kaylee. Among friends they are often called Kale or Kales. We often call them Kiwi at home, something that started years ago as just an affectionate play on the sound of the name. To go along with that, the rest of us got fruit nicknames as well. DS is Mango, DH is Papaya (kinda like Papa), and I am lemon (the closest sounding fruit to Mom). Kiwi and Mango get used often, Papaya and Lemon not so much. I do put the initial "L" on things when I am marking them as mine though, since K for Kim or M for Mom are not unique initials in our house.
