offering organization of name day parties specifically for children?
I would only like to point out that these businesses are just covering all their bases, as the typical phrase they use is "urodziny, imieniny dla dzieci", plus a host of other party occasions. I have brought up 2 kids in Poland (one is now early teens, the other late teens) and if you asked THEM what they think about having a name day party, they would pull a face at best. I should know, I had to organize all those birthdayparties through the years and think of gifts to buy for their friends' birthdays.
Name days are good for those who do not wish to disclose their age any more - and for those who are casting around for a reason to hold a party ;-)
But seriously - I have never personally heard of a nameday party held for a child. For my Dad, for auntie Flora, for my colleague at work, yes - but never for a child or teenager. Someone might say to a child "best nameday wishes" in passing, but that's about it. Birthdays are the big thing.