It was customary among many noble houses of Europe to repeat names of ancestors as a means of legitimizing the rule of their children by associating them with "past glories" so to speak (though it should be noted that regnal numbers as we know them today were not used prior to the 1200s). Hence why Louis, Philippe, and Charles account for 35 of the 50 or so French Kings.

Frederick is just a very popular German name that means "peaceful ruler", and as such was popular among Germanic nobility. Denmark just happens to like the names Frederick and Christian. That's the thing with traditions- the longer they last, the more important they become, and the more important they become, the longer they last.