Shorethings can verify, but I believe the permit goes with the property, not with the person or company who submitted the application. I wouldn't be surprised if you needed to sign something that allowed them to act on your behalf as the property owner. So you should be able to hire another company using the same approved permits, though you should check on how long the permits are good for before expiring.
The permits are public record and you can probably find yours on their website. It may give you all the information you need to answer your questions and talk to another company.
http://des.nh.gov/organization/divis...es/permits.htm