Even the current Queen's son is named Prince Frederick, and his own son Prince Christian, so the pattern continues.
While you're waiting for new responses, this question was answered well a few months ago and you might like to check out that earlier answer:
Follow-up question: I always wondered how the dynasties accounted for anything that might inadvertently break the tradition, like sudden deaths or other heirs being more fit for the job.
Like, did they have backup louises, henrys, fredericks and christians in case intended heir unexpectedly kicks the bucket? Or do they take the younger brother Antoine and rebrand him Louis when he ascends the throne?
And how many Fredericks and Christians were there in the Danish royal family who didn't become king?