An FCC ID is a unique identifier assigned to a device registered with the United States Federal Communications Commission.
Products intended for market access into the United States will be getting an FCC ID before they can enter the market. If you have more than one model name / number that would not make any difference for your application. You can list the model names you have in the certificate, but FCC does not look at model names or numbers. The only thing that is important for FCC certification is the FCC ID. The FCC ID should be put on the FCC label clearly to be seen. An FCC logo is not necessary.
The company’s legal name is not required to be on the label with the FCC ID. A product may be marketed under different trade names without re-filing for equipment authorization approval, since the FCC ID remains the same for identical products.
FCC IDs themselves are not serial numbers, but they can contain serial numbers. The first 3 to 5 characters of an FCC ID are chosen by the Federal Communications Commission. This is the body that approves the FCC ID certification numbers. The remaining characters of the FCC ID may be the same as the serial number or model number of the device.
Multiple FCC IDs for essentially the same equipment is permissible under 47 CFR 2.933 – Change in identification of equipment. The same equipment may be certified with different identification either under one applicants grantee code or for other applicants with different grantee codes, as long as all parties enter into an agreement. The rules do not require a change in FCC ID for equipment changes when only trade names or model numbers are changed.