In the time frame listed above, one must first take into account that this was before record keeping was just starting. In the case of NY, counting people wasn’t there first goal, extabliching at the town and county level who owned various parcels of real property so that taxes levied on the land could be collected from the proper owners-living on the land with a proper deed to show proof of ownership or were absentee owners or lots were unclaimed or no owner could be identified. In NY a state law requiring town clerks (of those towns that had been created) were required from 1799-1804. Having deeds recorded where the original owner lived or at the county clerk’s office was required to be filed. Until recording things became law, if the owner and buyer had a copy of the title to property, and the seller agreed in writing to warrant and defend the buyers ownership of the land in perpetuity.
When the federal census was started 1790 and up through 1840, only the head of household was named. Those with the personso named was M or F and free or slave. It wasn’t until 1850 that that census became to count and name everyone in a given household. Babies young than 1 year old were usually listed as infant.
So between 1790 and 1840 the federal census has the surname of the one who was the head of household. Some censuses were taken by the state on the half decade. For those counties created at the time of the state census. Some have survived and some have not. People moved a lot, I have noticed this movement was basically to “earn there salt” or went to wherever prosperity seemed to have set up shop or where opportunity has beconded