are you allowed to ask for personal (gashmyus)requests on yom kippur? I am aware that on Rosh Hashanna there is an inyan not to, does the same reason apply on yom kippur?
The reason we don’t ask for personal requests on Rosh Hashana (at least the first day), is because the integral focus of the day is being mamlich Hashem.
So, no, the same reason does not apply. Yom Kippur is a highly personal day of slicha and kapparah.