Who says it has to?
See, that's what I DON'T like. If you can come up with something GOOD, then I don't have too much of a problem with looking to incorporate the parents name into the horse, but I would MUCH prefer you come up with something original. To me, relying too heavily on the parents for inspiration shows a distressing lack of imagination most times.
Nope, didn't mean the name has to mimic the parentage -- the example of Periscope is an excellent example. You can be creative and still hint at the parentage. IMHO, I just thought the double "storms" in this particular individual's parentage would make for all kinds of naming ideas -- Storm Bank, Gale Force -- but Giant's Causeway? For the life of me, I can't figure out how they came up with that.
A couple of other strange ones that came to me today are Lemon Drop Kid (c'mon, for a racehorse?) and Black Minnaloushe (say what???). I have no idea what a "Minnaloushe" (sic???) is. Only mental image it conjures up for me is Snydley Whiplash's moustache. (And if you're not an old Dudley Do-Right cartoon fan, you have no idea what I"m talking about. LOL)