Complaint Review: International TVL Network

I booked a flight for the Philippines and call the service number to make a reservation. Upon booking, I've noticed that my name is misspelled by the agent. I call the agency to inquire and was told that the problem was fix therefore I should not worry. I was allowed to fly from South Carolina to JFK, but upon arriving at JFK I wasn't allowed to board the flight for overseas. I was told that my name is not the exact one I'm my ID and the flight information. I am now stuck in New York on going for 5 days. Me and my daughters have been contacting the customer service but with no avail. I was told that I have to but my own flight back home but they yet refunded I was promised. When we call, we are always told that someone will call us but they never do, we always have to call them. The calls will either lead to a voice mail or worst get dropped. I would have not board the flight knowing I cannot come back home.