To the best of my knowledge, the tab can't be hidden though it can be made harder to find under the 'More' tab (at least in Classic).
That being said, if you have request queues that contain sensitive data, you could look at altering the security settings on how access is granted to requests overall. There is a global setting in Setup for what happens to setup security for the person making the request, as well as what should happen to everyone in their company. If you have 'People from the same company' selected there, then all users in Company ABC will have an identical security level for that request for ALL request queues.
If you uncheck that box, then only the person inputting the request will see it (along with the receiver etc). That being said, that's a global change to ALL queues at once. If you want that impact on only certain queues, then you would make the global change, and then go into each queue and configure again there in reverse.
While it takes more work to configure queue by queue, it also does afford an admin a much more granular level of security controls for incoming requests.