We have nicknames and family lines. The nicknames are so much fun. Mine is Lola, like the lady in the song Copacabana. Trust me, it fit at the time
We also have certain items that are passed down from big to little that have been around a long time. Our big family line gift is this handpainted barstool that the first person in our family line painted. Each time someone in the line gets a little, we add their name to the stool. It's really cool.