I am looking at a used PS3 that has a digital game, but I don't want the PSN account. Is there some way I can keep the game and have my own PSN account?
No. Purchasing a PSN game inextricably ties it to the account on which it was purchased.
You can, however, leave that user on the PS3, still linked to that online account, and any other local users on that PS3 (whether linked to a PSN account or not) will still be able to play that game and have their own separate saves and trophies. But if you do this, that PS3 will continue to count against that account's limit of 2-5 (depending on the game) allowed devices, which the original owner may not care for.
If the original owner is willing to give you his PSN account, there's no issue here; make sure you get the password and so on, leave the PS3 linked to that account via its local user, and set up your own separate user on the PS3 linked to your own PSN account if you wish.
If the original owner wishes to keep his PSN account, he should almost certainly disconnect that PS3 from his account and you won't be able to play the game.
Unless the game was pre-installed on the PS3 as part of a deal or special offer, it isn't possible to use a different PSN.