You only need to provide your first initial and last name to fly

Right in with the recent news that the TSA wants to collect full names, birthdays and genders as part of secure flight is the indication that currently you only need to provide your first initial and last name.
Does this mean that the airline only passes on your first initial and last name to the TSA, or do they pass along your full name if you give it to them?
Either way, I assume this means that you are free to provide the airline with only your first initial and last name.
I have always given my full name to the airline, but that meant that when the TSA recorded my boarding pass information as I chose to fly without ID, they got to record my full name because it was on my boarding pass. Although I have an uncommon last name, I would really prefer to only give my first initial and last name, and leave off the chance of the TSA keeping records that identify me more fully. Not for any good reason, just that it freaks me out that the federal government is keeping records of my movements.
Even if the rule does go into effect, providing this additional information would be optional.