Can I use Company E-verify number of NC branch to continue working in TX branch of the same company?

My company says, their NC branch is E-verified but not the whole company. They asked me to use their Company ID number to apply for OPT extention. Can I do that? Or do I have to treat my application as "changing company " and then enter the same company name but NC address and then their E-verify number?

Well, I do not know. I suggest you call USCIS customer support for E-verify and check with them.