In this final section of the teshuva, Rav Moshe discusses how we write the name of a שתוקי or an אסופי into a כתובה. These two categories, listed in the first mishna of the final chapter of קידושין, refer to individuals whose parentage is unclear and therefore their acceptability to marry a Jew is questionable. A certain city apparently had the practice to write their names followed by בן אברהם אבינו, similar to what is done for a convert. Rav Moshe ruled that such a practice should be stopped, since it would call into question the כתובות of converts if all of those categories of people would be labeled the same way.
Rav Moshe also objects to writing the mother's name, since that will potentially lead to confusion whereby one might think that the individual is from a Jewish mother and a non-Jewish father and will wind up allowing them to marry another Jew or even a Kohein.