As you create a new Request, you will be given the option to mark your Request as Private. The default will be for your Request to be Private, and leaving this toggled to On ensures that only you have access to view this Request and its results.
Your Requests that are marked as Private will be denoted with a lock symbol.
Your Requests that are not marked Private will simply lack this symbol and will be visible to teammates when they view the ReMind dashboard.
If you have a previously-public Request that you'd like to convert to Private, this is possible using the "Edit Request" option: