I live in a shared house in NYC and there have been some issues amongst roommates. No one in this house was on the original lease from the landlord as people have moved in/out replacing those people throughout the years.

I am the only registered/documented bill payer [Con Ed Electric] for the house. Does this establish me as the legal month to month leaseholder of the house? Or is every tenant have their own individual month to month lease with the landlord?

individual month to month lease

Oxymoron. You don't have a lease. Each occupant has a month-to-month tenancy; no long-term rights at all.

Your arrangement with the power company is immaterial.

A lease is a contract which gives you rights more extensive than occupancy at will. You don't have that. If the landlord wants to throw you out you have no lease to protect you.