Can you keep any reserved card hidden from the other players
Definitely. You can keep the information to yourself. That's the point of the hand. There would be no point in drawing a card without showing it to others only to place it somewhere others can see.
Must you keep any reserved card hidden from the other players
This is the interesting question.
A rule on whether you can share private information is rarely stated explicitly unless it's forbidden because the game sees keeping the information private as an advantage for you, so the default position I take is that you can share private information as long it's not explicitly prohibited.
Unless the game has some kind of team or co-op element, when a game indicates that information is private except for one player, it's for that player's advantage. They won't mention that you can reveal the information because there's rarely any reason to do so.
Rules clarifying that you can share private information would usually be found in tournament rules, not the game's rule. For example, the Magic: The Gathering tournament rules include the following passage:
players may choose to reveal their hands or any other hidden information available only to them, unless specifically prohibited by the rules.
I feel that's the default position one should adopt for any game. Games where information must absolutely be kept secret will state this. In Splendor, I wouldn't hesitate to show a card I had reserved if I had a reason to do so.