Here in New Jersey, your Electrical Contractors License allows you to work statewide. WE have two (2) "licenses"; Licensed Electrician and Licensed Electrical Contractor. The "Electrical Contractor" is actually a business permit. The Lic. Electrician has to apply for the business permit. If you change your business name, or open under a different name, you have to obtain a new business permit.
The license number for the Lic. Electrician remains with the individual for life, or until you "retire" it. When you change the business permit, they add a letter at the end. (ie: BP # 8209-A) I changed from a sole proprietor to an LLC, and had to go thru the process.
Various towns, cities, etc., have requirements for "licenses" for tradespeople (carpenters, siders, roofers, etc) The electricians and plumbers are exempt, as we have stste licenses.