You will be paying State taxes on where you live and work.
The company you work for can be located anywhere, and where the headquarters or office you are assigned to does not matter.
You say you "will" be moving, so make sure the company knows when you move so that can switch you from NJ to SC.
The year of the move you will have a partial year NJ and partial year SC returns to file, and then following year after that just the SC return.
You will be paying State taxes on where you live and work.
The company you work for can be located anywhere, and where the headquarters or office you are assigned to does not matter.
You say you "will" be moving, so make sure the company knows when you move so that can switch you from NJ to SC.
The year of the move you will have a partial year NJ and partial year SC returns to file, and then following year after that just the SC return.
NJ is one of a few states that taxes telecommuters (and has done so for years), so you must continue to file there:
https://www.journalofaccountancy.com/issues/2009/jun/20091371.html
https://www.thetaxadviser.com/issues/2010/feb/apractitionersguidetothetaxationoftelecommuting.html
http://www.koscpa.com/newsletter-article/state-tax-consequences-telecommuting/