Upvote:2
As I said in a comment, it will most likely be possible to have your baggage checked through all the way, even on different bookings, if you inform the check-in staff in Osaka that you have a connection (they will probably ask you about it, as well).
Assuming it's not possible, however, with more than three hours you have more than enough time to treat your flights as completely separate: collect your luggage at the main collection point in the arrivals area as if you did not have a connection, and proceed to the Delta check-in counter in the departures area as if you had arrived to the airport by train or whatever. Everything will be clearly indicated.
If your incoming flight is delayed, inform airline staff as soon as possible and they will do what they can.