Issue with Name Change on Turkish Airlines Ticket

I created an account with Turkish Airlines 8-9 years ago. When I created this account, I used a different name. While purchasing tickets, I always proceeded without using the membership name. Yesterday, while trying to buy a ticket, the system froze at the 4th or 5th step. When I tried to purchase the ticket again, the price had increased by ₺1450. I saw the original price on my TK account, so I bought it from there. However, my name was incorrect, which means I won't be able to board my flight. The customer representative said they could only correct it if there was a single error. Both my first and last names have errors, but they said it couldn't be corrected. Because of this, I won't be able to board my flight. They told me that if I buy a new ticket, my money would be refunded. The current price of the ticket is ₺4500, which means they will take an additional ₺2000 and refund my money. How can this not be corrected with 2 days left before the flight? They will just take the extra money and sell the ticket to someone else. I want this issue to be resolved quickly by Turkish Airlines officials.