The papyri- which date from the post-Exilic period- show that intermarriage was not unusual and, according to Porten,

... took place in the families of the lay leadership and Temple officialdom. Having long since adopted Aramaic - the lingua Jranca of the Persian Empire - as their spoken language and the language of their private letters and notes, the Elephantine Jews were apparently not overly concerned that their children could not speak the language of Judah. Untroubled by the fear of a second expulsion from the promised land- a fear which plagued some of the pious of Judah - and united around their own Temple, the Elephantine Jews apparently felt capable of absorbing a small number of pagans into their community. (2) Intermarriage between Jews and Gentiles was not infrequent in pre-Exilic times but it became a controversial issue after the return from Babylon. In post-Talmudic times it was rigorously forbidden by the rabbinic authorities unless the non-Jewish partner was converted strictly in accordance with the laws of the Halachah.(3)

There must have been some ceremony by which a newcomer indicated abandonment of his polytheistic practices and adoption of Judaism. The pagans who intermarried in Judah apparently became Jews. Those who wanted to join Zerubbabel in the building of the Temple claimed 'We worship (seek) your God as you do' (Ezra 4,2) ... Two distinctive signs of the covenant between God and Israel were circumcision and the Sabbath and it is likely that circumcision and Sabbath observance were required of male proselytes. The fact that Egyptians practiced circumcision and that some of them refrained from eating pork (Herodotus 11,47) may have served to facilitate proselytization. One marrying into the Jewish community might adopt a Hebrew name, not as a ritual of conversion, but as a matter of onomastic assimilation ... Many who intermarried did not change their names; however, they may have had two names as Jews had elsewhere in the diaspora. (4)

(1) ibid., p. 133.
(2) ibid., p. 350.
(3) cf Peake, 332f 'mixed marriages were never so strongly objected to by the Jews as they were by their political and religious leaders'.
(4) Porten, p. 251.