The page names are created in CMN_CAPTIONS_NLS at the point when the object is created.
Even renaming the object later on wil (unfortunately! I think this is a bug in Clarity) not change the page titles / page labels everywhere.
It seems that you have no other option than to manually update CMN_CAPTIONS_NLS -- taking care not to change the references but only the display text.
We had the same hassle when the customer asked us to slightly relabel a custom object we had created.
Especially with the "Idea" object, though, I'd be extra careful. This is part of Clarity core stuff (sometimes handled in a "magic" way) so you will also find that for instance there is a "magic" field in other investment objects: "Originating Idea". If you're going to re-label the Idea, you'd also have to address these places in a consistent manner. Frankly, I'd try to talk the customer out of this :-)
Daniel