During domestic travel it might not affect but as you are travelling to I'national that may be troublesome so better correct the name instead of facing any future problem while migrating.
I had the same issue while boarding flight from Banglore for Pune. and there as well I had to buy new ticket on the spot. They did not let me go with the ticket I had with the incomplete name. So, it will be obviously problem for International flights.
You name on your Passport should match exactly with your name in your flight ticket. Also, you cannot change your name on your flight ticket without cancelling it as none of the flight operators allow it.