Steven
There are no Corbetts in Durham in the 1851 census although an English one does crop up later.
My photocopy/xerox is 20 years old.
Say the word "Cubit" and remember that the enumerator wrote down what he heard, and they were Irish, straight from Clare
Johana is an alternative to Jane (the Sunday Latin name). She used this and Jane through the Catholic Church censuses, the National Censuses and the Baptisms, marriages and funeral entries that I viewed.
I was concerned , like you, when I could not find Corbetts and glad when they turned up. You will note that they have living with them Derby O'Connor (Jane's surname is O'Connor or Connor depending on who has written it down) and Bridget Doherty. The baptismal entry for Michael Corbett reads "Born March 10 1852. baptised March 14 1852, Michael Corbett son of Patrick Corbett and Jayan nee O'Connor his wife. Michael O'Connor and Bridget Doherty are godparents.
Other O'Connors are nearbye, in Framwellgate and they show in the Church registers
Patrick's occupation is constant in everything - shoemaker.
Subsequent censuses confirm the details. By the way they are down as "Cobbet" in the 1854 Census of Roman Catholics and a Jeremiah Connor is with them.
Anyway, I, and another cousin working independently are satisfied and there is no alternative.
You will find with family history reseach that, as you go back in time the population decreases, the quality and quantity of the data decreases, the level of literacy decreases and the social standing becomes marked. So when a middle class, educated, litterate priest or census enumerator asks a question of a poor Irish country man barely living in a strange industrial town the answer will be documented on their perception of what they have heard and a desire to move on. Remember also that at the time there was racial discrimination against the Irish.
A point worth mentioning is that I, after 140 years, would have been the person checking the entry for accuracy.
I have found that in nearly every case a Corbett in Durham is a relative of mine.
I bet you wished that you had not asked.
Gordon