I was always told that your name must match your passport. I always enter my First Middle and Last Name in full with no middle initial(the full middle name). on the boarding pass due to the room provided they shorten it. For instance Mr. John Brandovich Davis-Smith might read as Mr. John/ B. DavisSmith etc.

I think your full passenger data is sent to the TSA/Department of Homeland Security just to be sure you are not on the "no fly list". If you were not on the no fly list it does not matter what appears on your boarding pass as you would not have been allowed to check in if there were issues with your name vs the no fly list.

It boils down to this provide your full name no matter what . If your Drivers License says B for your middle initial and your passport has your full middle name it should make no difference. This is the reason why my California State ID and Passport have the full first middle and last name.

Hope this helps.