I have received about 20 orders recently, where every transaction was declined.

The person signed up for our most expensive account.
They used 20 different credit cards.
Each transaction attempt was declined as fraud.

Now, I can see information such as the cardholder name, address, etc...

Do you think it is the "right" thing to try and contact them and let them know someone is using their card?

Yes its always a good idea IMHO. Its your good deed for the day and most people are surprised when I tell them their CC was being used

Rgds

Rus

Sure I do it all the time.

Yes & make sure to report it your CC processor if they already did not catch it. They will grab the IP address, report it to Visa or MasterCard & then MasterCard will contact the ISP

I report it to our CC processor, the owner if we can find them and the ISP the order came from. Also, save your documentation in case the CC issuer needs to contact you for additional information.

I think you should contact the credit card company and let them know... things will get done directly.