I'm with foodpump on this
A Chef is in charge of the kitchen whereas a cook is in charge of his or her station.
Of course, once you move into the bigger hotels then even the Chef or Exec. Chef will have little to do with purchasing (as this will be done via the purchasing department in order to get the best deals - as they don't only buy food but everything the hotel needs).
Still - the Chef or Exec. Chef still needs to work closely with said purchasing department to make sure they don't just buy 2000lbs of quinoa with nothing to go with it :)
Simply put, in all my years working in the industry, you are a cook as long as it is not your responsibility to manage the food cost :)
As for the OP's question - it is your business. Technically you are responsible for every aspect of it.
I would rather go with the title Owner (as that is really what you are) but if it gives you an edge, sure, go with Chef.
Don't think anyone will challenge you based on that.