It's the latter. The accent doesn't change. They are still type1 /コ]ヤマ/ and type1 /リュ]ウ/. Notice that Shinobi is not her surname, and Hime is not her given name, either. That's why "Shinobi Hime" acts like a compound word "Shinobi-hime" as same as かぐや姫 or 親指姫.
Incidentally, if Shinobi is her surname, the accent is type 1 /シ]ノビ/. Similarly, if 小山竜 is a compound word, it's type 3 /コヤマ]リュウ/ (and this word is interpreted as a kind of dragon, not a combination of surname and given name).