There's no restriction on creating additional accounts as you see fit, including for this purpose, provided that you don't use multiple accounts to allow you to do something you wouldn't be able to do with just one (e.g. voting for yourself).
In fact, we've had a user PSE-famously "leave the site" only to start posting puzzles on a new id, thus starting a several puzzle long meta-puzzle that ended with a reveal of who that new id actually was. So creating new account(s) for the purpose of a puzzle is fine, again provided you don't use the account(s) to do something you can't do with a single account.
You can obviously delete those profiles once the riddle is solved, but it breaks its magic a little.
But this is wrong. We want to make sure puzzles (and answers) here are self-contained, rather than relying on external links to information or resources that may change or disappear. Remember that your puzzle may be seen and attempted by someone looking at it years in the future, and it should still be possible for them to solve it from what is provided within it.
If you build a puzzle around information in a user profile, whether it be your posting account's or some other account (whether controlled by you or by someone entirely separate), then that information becomes part of the puzzle and now cannot be changed or deleted without harming the puzzle (see Your answer is in another castle: when is an answer not an answer?, for example, for a deeper look at why posts on SE should be self-contained).
So you can NOT delete those profiles once the riddle is solved, because it breaks the riddle a lot.