I would feel extremely uncomfortable about this, op. To the point where if my sil did it, I would serious consider changing my child's name.
To me, it assumes a relationship that does not yet exist between niece and aunt, and is possibly unlikely to considering she lives far away. It's also very intimate.
But moreover, I've known several situations where tattoos of children's names or faces on family members have caused enormous upset. The worst scenario was where the baby in question sadly died and the mother just could not cope with her mil having the child's name on her arm where she could see it: made more complicated by the fact the tattoo made the mother feel that the mil had somehow taken ownership of the memory of the baby through the tattoo.
And then, of course, it became even more problematic because of the emotional meaning if the mil had the name lasered off.
I've also known awkward situations where couples have split and started new families, and someone has one child's name tattooed but doesn't do the others.
It's just asking to open a can of worms later down the line. Life is difficult enough without doing something that has the capacity to blow up.
I know it's the aunt's body and she can do what she likes. But sometimes, it's the meaning and intention behind an action that gives pause, not the action itself.