I have my childrens initials tatooed on my wrist -very tasteful and I will never regret it as they will always be my children.
I actually love glancing at their initials -not that I need reminded but it makes me closer to them given they work fulltime and dont have the same opportunity to see me nor me them
I am very proud of that tatoo and so are they -it made them feel special that I would forever have their initials -litlle do they know I have even more permanent marks -stretch marks but hey they dont have to see that do they lol
If I have kids then yes maybe theirs, I would never get a partners name tattooed on me and would never let them have mine tattooed on them.
I did buy my last girlfriend a tattoo for her birthday, but she had been saying she wanted it done for a couple of years and it wasn't a personal one at all.