In discussing the reliability of witnesses who had signed a contract, we find Reish Lakish asking Rabbi Yohanan how to deal with a case of witnesses who sign using non-Jewish names. Rabbi Yohanan responded by relating a case where a contract came signed by two people named Lukus and Los, and it was accepted. The Gemara continues that giṭṭin coming from the Diaspora are accepted with signatures that appear to be non-Jewish names, since we know that many Jews in the Diaspora have such names.
Many of the rishonim, including Rashi, understand the original question as dealing with a case where the get originated in Israel, so it was not necessarily accompanied by a messenger who could testify that the document was written and signed in his presence. Based on this understanding of the case, one of several different questions may be dealt with:
The Ramban brings an opinion that the question is whether we must be concerned that approving these names in our case – when we know that they are Jewish – will lead to a mistake in other cases where, perhaps, they are not Jewish.
The Rashbam suggests that we are not sure as to the identities of the witnesses and we are afraid that the people who wrote the get may have allowed non-Jews to act as witnesses, perhaps because non-Jews can act in this capacity regarding other legal documents (see daf 9).
As far as the names themselves are concerned, we know that Greek, non-Jewish names were commonly used in Israel during the period of the Talmud – even some of the sages had such names, like Antigonos of Soko. Nevertheless, most names were Hebrew or Aramaic. From the archaeological finds in the large cemetery in Beit She’arim, where many Jews were brought for burial – often from foreign lands – it becomes clear that Greek and Latin names were commonly used in Jewish communities given the large number of such names found among those interred there.