The Brokkens said they had handed over their passports with their full names on it to the agent and Ms Brokken had flagged the misspelling of her name previously.
Mr Brokken's name on the ticket was 'Hank' - the nickname he had introduced himself as to the agent - and Mrs Brokken had been entered as 'Aloyse'.
"All my life I've been called Hank. So if I introduce myself to someone, 'I'm Hank. Pleased to meet you'... but not on official paper,' Mr Brokken told the Seven Network program.
To travel internationally, names on passports must match up with names on the tickets or bookings.
'The one and only thing in our lives what we would do right or perhaps enjoy, perhaps really good was all of a sudden not possible any more,' Mr Brokken said.
"I just felt sick and perhaps a pain in my chest."
His wife added: 'We never really had a holiday like that or anywhere else for that matter. We never went to hotels or went for a fortnight somewhere.'
Mr Brokken had a history of heart disease but his doctor had given him the green light to go on the trip.
But after finding out about the bungle, the couple said the stress of the news caused Mr Brokken to have a heart attack.
Unfortunately the couple had to cancel their trip.
To add to their woes, the Brokkens tried to claim back their holiday from their insurance company but they were refused due to Mr Brokken's medical history.
Flight Centre has admitted to the mistake but denied responsibility for the heart attack.
"A spelling mistake was made in the booking. We believed we could resolve the problem relatively quickly," a spokesperson told Today Tonight.
"It wouldn't have affected the customers' travel plans had they been in a position to travel the following day."
The couple want Flight Centre to refund the cost of their trip.