I went in reverse:

I sent an email to GE, and then actually followed up and CALLED GE in D.C. (pretty sure it's there) a few weeks later, since a name change can take several weeks.

I explained that I screwed up and should have used an initial instead of my full middle (to match my passport, which has initial only). They said that it was in process, made no guarantees, and were relatively friendly about the whole thing.

A few weeks later I received a new GE card with initial only