Here’s what happened using a common “Jewish” name, Irving:
In the early twentieth century, a lot of American Jewish parents decide that it would be a good idea not to give their children obviously Jewish names. They instead chose a name that they think is typical of non-Jews. They often have an alternate (probably Hebrew) name for the child that can be used for certain Jewish rituals and that the child can change his (or her) name to if as an adult he (or she) really wants an obviously Jewish name. Since many Jewish male babies had an alternate Hebrew name of Isaac, it became common to give the name Irving to them on their birth certificate, since this preserved the initial at least.
Now Irving was never before that time thought of as a Jewish name. It’s clearly a standard English name, if not a particularly common one. But the effect of so many Jewish babies getting the name Irving is that it now becomes common to assume that any child named Irving is probably Jewish. Because of this, American non-Jewish parents decide that they shouldn’t name their baby Irving since people might assume that he is Jewish. By the mid-twentieth century, there were almost no non-Jewish children named Irving anymore.
So Jewish parents decide that they shouldn’t name their children Irving either since everyone will know that he’s Jewish. Irving almost completely disappears as a first name for children. Jewish parents have assimilated enough by the late twentieth century that they tend to chose the same sorts of first names as everybody else (or, at least, as all other middle-class to upper-middle-class white people) in the U.S. A few Jewish parents go back to giving children names like Isaac that are clearly Hebrew.