Sign up PSN account
I was unaware that there was no way to sign out and use a different account on a PSP.
That's because there is a way. But you can't just switch between PSN accounts on the PSP, the way that you can on the PS3. The PS3 is designed to be shared by multiple people that each have their own PSN account. The PSP is designed to be used by one person, using a single PSN account. If you want to change the account that you are signed up for Playstation Network with on your PSP, use the XMB>Settings>System Settings>Restore Default Settings command. That will allow you to Sign up for Playstation Network again with a different PSN account. Doing so will not delete any of the save data on the PSP, but your multi-player save data may no longer work if you change the PSN account that your PSP signs in to the Playstation Network with.
None of your PSP game save data is stored on your PS3. The only save data on the PSP that can be copied to the PS3 is save data for PS1 Classics, or Minis. Using ad-hoc multiplayer via a PS3 doesn't change this.
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