Calculate date for ordinal day of week in month
For the parameter, may I suggest nthOccurrence? Alternatively, anything that communicates what exactly it means should be alright, given that it's at a pretty contained location - even nthTimeDayOfWeekOccursInMonth wouldn't be terrible, especially since dayOfWeek and month are also parameters.

The method is harder, mainly because the thing you're calculating doesn't have a great name. "Return the nth occurrence of a weekday in a given month of a given year" doesn't lend itself to brevity. I would take one of two routes:

Does the assignment / class / professor have a term for this functionality? "Weekday oracle" or something equally obscure works perfectly if it's the way that everyone else who will see this code knows to refer to this thing.

If not, I would name it what it is; something like getDateOfNthTimeDayOfWeekOccursInMonth - this would pair well with naming that first parameter nthOccurrence. In this case, I think information (what exactly can I expect this to do) trumps brevity, because what it does is not very common / intuitive.