That's only scratching the surface. What happens when a baby pony grows up but it's name is still baby (insert mom name) is that pony just stuck living in its moms shadow?
I believe it was said in the comics, but the babies who share their mum's names were made from their mothers' reflections in a magic mirror? I assume that babies born naturally don't share their mothers' names/look totally identical haha, but as for the mirror babies, I guess they'd be (ponyname) Jr, like it is with humans who have identical names to their parents