Still very common during the War of Independence, especially among the rural population. Although it would during the War of Independence become very marginalized as "Roman" came to be associated with a pro-Ottoman or obedient Greek, as Roman was what the Turks called them. The obedient enslaved Greek answered to Roman and the patriotic, proud Greek answered only to Hellene it was said.I have heard that some Greeks were still calling themselves Romans all the way up to the early twentieth century. Does anyone happen to know how common it was at this point?
Although as said, at the time this didn't really go much further than the educated elite and the Greeks who remained Ottoman subjects would still largely call themselves Roman. One of my favorite quotes about this subject comes from the memoirs of Yannis Makriyannis who noted the following question one of his friends had posed:
"What say you, is the Roman State far away from coming? Are we to sleep with the Turks and awaken with the Romans?"