In reviewing your original question and your follow ups, I don't think we or you really know what your question really is. What you call yourself is not the issue, what service of value you can provide is the issue. Details, such as where you're located and then what type of services you're going to provide would help us.
The answer to your question above is yes. Just as you are an electrical contractor, if you're going to do drywall, then you could be a drywall contractor. For some services or trades, you may need certain licenses, but that is dependant upon where you're located. The there is permitting, again depending on scope and trade and dependant on local requirements.
I think of being a general contractor, in that you provide an array of services, but certainly or not necessarily all. Some builders, would sub out near most of the job, but they would be considered general contractors. Whereas, 'contractor' I think as singular service.
I guess in the end, I just don't understand your preoccupation with the terminology for your situation. Others have offered responses, but you only return with more of the same question. :confused1: