As an example: I was born in the United States and would say, "I am an American."
Since Igbo is a designation applied by Europeans, I don't know if someone would say "I'm Igbo." In the early 1800s, Nigeria didn't exist as a country yet. There were kingdoms such as Onitsha, Nri Kingdom and Arochukwu, but I'm having trouble finding out how someone from one of those cultures would describe themselves when speaking to someone from another area.
tweeted a friend of mine who is a profesor of african studies. His focus is more on South Africa, but this was the best he could come up with (an no one else has weighed in):
they may have used the term Nri; more than likely they would have just claimed their place of origin (i.e. Nsukka)
a useful book might be Thornton and Heywood's Central Africans, Atlantic Creoles and the Foundation of the Americas, 1585-1660