The PSP is a little weird because accounts aren't tied into the system the way they are on the PS3 and Vita. You basically have your PSN log-in credentials and what acount the system is activated under, but they can be completely different.
What I used to do with my PSP was just do all my downloading on my PS3 (which easily supports multiple accounts), and then when I copied the game over to the PSP it gives the option to change its activation right then if they don't match up. You can access the store directly from a PSP, of course, but it wasn't really made with multiple accounts in mind so you would have to manually re-enter everything whever you changed back and forth.
Of course it's still easier to swap accounts on a PSP than the Vita, grr.