Not unless you get a license from the company to do so. Being a non-profit is irrelevant.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
Possibly animal food regulations aside, you are dealing with principals of ordinary commerce. You don't get to pass off something as yours. You can ask permission and probably will have to pay for the rights. You have not explained how you pay for the bulk product or whether you charge for the repackaged product. Neither matter regarding the passing off issue. You should contact a lawyer for advice based upon all of the facts.
The advice provided is in good faith but not a guaranty of accuracy under all circumstances.