Oh yes, she did!
BSMP is the name. And her initials.
Thank you Rachel Maddow: "On Rachel Maddow's show Tuesday night, Maddow dug into some curious paperwork filed in Alaska last September by the 19-year-old Bristol Palin, daughter of Sarah, mother of Tripp. The paperwork established Bristol Palin as the organizer of a new company called BSMP LLC. (BSMP is Palin's initials: Bristol Sharon Marie Palin)."
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