FCC Re-certification if the brand name and outer casing changed?
FCC testing usually includes rf testing of the unit in the case, unless it is a certified modular device. Changing the case will likely require retesting, and certification.

Keep in mind that even generic device's that are rebranded, only cosmetically, will often have their own fcc id. That's for devices that don't have case changes too.

Of course we are not lawyers, and the fcc process comes with heavy legal implications. Consult a lawyer. They may just say to recertify as a precaution. An upfront potentially unnecessary  cost is easier to deal with than a large unforeseen fine or recall.