so there's two reasons you would want to do this:
1) there's a privacy issue and users should not be able to see each other's requests
this would be solved by your sharing settings and the way you configure your queues, and can be addressed in any number of ways there, the most common of which is to simply not allow requesters to view the project that holds the requests.
2) it's very confusing for users to see a bazillion requests instead of just theirs
this would be solved by you creating a dashboard that is nicely named, e.g. "click on me!!" or "only my requests" or something like that, that would only show their requests, and moving the Submitted section to the bottom of the list to make it less likely to come up first. You can also train users to use the right filter, or submit an Idea that users do not default to "All" when they click on this section.