If you haven't started working yet, there's still time to negotiate this. I've hired people who have told me, as soon as they accepted the offer, that they need a certain day/week off within the first three months of employment. We accommodated them, although they got the time off without pay as they had not accrued vacation time yet.
So ask. But if this is a popular day for people to take off, be aware that your new department may have reached its limit of people out for the day months ago. Many places I've worked have had rules that only a certain number or certain percentage of the department could have scheduled days off on the same day. For example, out of a department of 10 people, only two could schedule vacation days at the same time. That left eight people working, which gave us enough flexibility to cover if someone went out sick. We could get the essential work done with seven people, but with less than that it would mean tons of overtime.
So ask and hope for the best. And if they can't give you the day off, surely your father will understand that having a job is very important.
This shouldn't hurt you in the long run, if you make it clear that it is a specific day for a specific purpose--a ceremony honoring your father.