someone with my exact same name

I arrived late to the airport so I asked asked the airline to change my ticket to the next flight.Boarding went normal but when I was about to sit down there was another person with my same first name and last name was sitting in my seat.May it be identity theft? Impossible! it all happenned so suddenly.Turns out that while changing my ticket to another flight, the assistant saw my name on the flight already and did nothing, just told me I was good to go.I had to take the flight after.