If anyone is curious, it looks like my SkyBonus number from two companies ago was still entered into my account, and I was getting offered that as my "Business" profile.
My Profile -> Flight Preferences allowed me to delete the old program. Logging out and logging back in shows no more Personal/Business at all, and life is good.
Oddly enough, I do work for another company that has negotiated deals with DL, but I'm guessing it's not via the SkyBonus program.