What is written in the machine readable zone (MRZ) on the passport card? If it contains the full name, then I wouldn't worry about it. If it has just one initial, then I would contact the passport office and ask them about it. They changed the passport card format recently, so they may have decided to do like on the Green Card where there is a middle initial in the bio section and a full name in the machine readable zone.
My passport card (issued in 2009) contains my full name in the bio section and in the MRZ.
