Given that Judaism respects all societies that behave in a morally correct manner, it is far from its ethos to push people to convert.
There have been times in Jewish history when Jews too engaged in a certain amount of proselytising, but over the centuries and particularly during the exile from the Land of Israel, Jews became more concerned with those who belonged to their own communities than with others.
Nevertheless, it has always been possible to convert to Judaism. According to traditional belief, a true conversion requires certain conditions: the person must have studied Judaism and demonstrate a sincere intention to live a Jewish life, and at the time of conversion, they must immerse in a mikveh, or ritual bath, and, if male, undergo circumcision.
(…) Upon becoming Jews, converts adopt a Hebrew name. Since Hebrew names also refer to one's father and mother (for example, Ben Yosef, “son of Joseph”, or Bat Esther, “daughter of Esther”), a convert's name generally traces back to Abraham and Sarah, as if they were children of the patriarchs: for they are considered not only the first Jews, but also the father and mother of all nations.
Source: "Per conoscere l'ebraismo" by Daniel Taub