I am being offered to do a rehab job that the homeowner already has a permit in his name. First time I have encountered this situation.
Question
Am I allowed to work under his permit or do I have to get my own?
For a rehab project you normally start with a building permit and this is obtained by the homeowner or a GC.
A GC would be required to use licensed sub contractors but he really holds the permit for the job. In most areas a sub contractor just signs-in as the contractor of record( plumbing, electrical, HVAC) and the permit fees are paid for by the GC.
A homeowner can pull the building permit and actually do the work himself to include the licensed trades.
Normally you could not work under a homeowner's permit without signing-in as the electrician of record.
The only way to know for sure what is required is to call the authority having jurisdiction/permit office and ask them. They may or may not require you to sign-in or even pay other fees.
The inspections are normally easier if they know who is doing the work and that person is a licensed electrician. Deal with the inspectors directly and don't let the homeowner get involved.