I don't know of any database covering all of them. You might have better luck trying to contact the ODFI to see if it can give you some help.
The ODFI has to give you the name of the Originator and the phone number. All you need is the company ID and possibly the trace number from the ACH reports. Go to
FRB ACH Participants Search , enter the partial routing number of the ODFI - the first 8 digits of the trace number - and it will give you the phone number for the ODFI's ACH department. Call it. Many large banks have automated solutions when you call, others just answer the phone. Tell them you need the name and phone number of one of their originators. They may want the company ID, trace number and sometimes date and amount of the transaction. Then they'll give you the phone number.
Then you can even call the Originator and see what other information you can obtain.