Sorry – I asked this before, but the reply said I wasn’t clear. Let me try again:
Let’s say a Shul has Kids Minyanim in the basement on Rosh Hashana, that Parents pre-register their Kids for. For security purposes, the shul has 2 non-Jewish employees to check the kids into the minyanim on RH. These 2 non-Jews have all the pre-registered kids names on a list. Now, let’s say a kid shows up whose Parents forgot to pre-register the child, so the child’s name is not on the list. To keep track of children, the 2 Non-Jews need to ask the Parents for the child’s name. The Parent gives the child’s name to the Non-Jewish people checking kids in….and the Non-Jews write the name on the list. Is the non-Jew writing the name a problem? What if the Non-Jew needs to ask how to spell the name? So the Jew is specifically telling the Non-Jew HOW to write it.
It is still not clear to me why they have to write the kids names down, therefore I will have to just answer you in a general way. The rules regarding a non Jew doing melacha for a Jew are the same for Yom Tov as for Shabbos. The rule here is, that if the non Jew is doing the melacha for himself he is allowed to do it, but not if he is doing it for the Jew it isn’t. Therefore if the non Jew is writing the names down because he is responsible to keep track of the children, then it would be permitted. Even if he is required to give the shul a list of the names after Yom Tov and if he can wants to remember the names and say them over after Yom Tov he may, but he is afraid of forgetting and therefore he is writing the names down, that is also alright, because he is writing the names down essentially for himself. However if he is doing it so only for the purpose of the Jews, then it would not be permitted, to allow him to write for us on Yom Tov.
I hope this answer your question.
Have a kesiva vchasima tova.