Lucy likes being married, but not for an extended period of time and she, through marriage and divorce, has been Lucy White, then Brown, then Black, and finally, Blue. Her SSN will match with any one of those names as long as she has kept SSA up to date. Thus, if she does, you don't have an IRS reporting issue. On the other hand, if she keeps them in the dark on her serial monogomy, her SSN will still match to Lucy White; i.e. there will be no IRS reporting issue or penalty assessment.
As long as you have a reasonable belief that she is who she says she is, you don't have a BSA issue either. As a personal opinion, I suggest you require that any account you open must be in the name for which she has valid identification, but I would not push her to produce a conforming SS card.
Outside of any expertise that I would claim, I suggest your issue concerns the validity/priority of your security interest if it is not filed on the "best" or "most accurate" name your borrower has.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.