FCC Frequencies

This is probably a simple question, but I've never thought about or looked into it.

Once you have licensed FCC frequencies for a base unit, are they specific to the unit/applicant, or applicant?

Example - I supply the company submitting the application with the details of the GPS unit that will act as a base.  On my behalf, they apply for and get permission to use frequencies with the FCC.  I use that unit for a while, but eventually have to replace that base unit.  Is it just a matter of buy a new unit and input frequencies in it because it is similar in nature to the replaced unit or was there a specific tie to the radio in the first unit that requires some form of update with the FCC?