Conservative Jews
The question as phrased in problematic because the word "mainstream" implies most common or most central. While Conservative Judaism is the most conservative of the Liberal branches of Judaism, it is certainly not the most common form of Judaism: Secular/Reform Judaism is.
Another view:"Mainstream" is, admittedly, usually defined as majority. However, if we define it as that which represents and continues the stream, it could be stated that Orthodox Judaism can claim this title, since its tradition is that it represents the beliefs of the Prophets and Sages all the way back; while the more liberal groups of Judaism do not claim to have been handed down their beliefs from such early groups as the Karaites or Hellenizing Jews. Nor did Karaism or the beliefs of the Jewish Hellenists exist before they were specifically promulgated, long after the end of prophecy.Judaism is called Judaism.
They are called "Jews".
The whole Reform Judaism movement in Europe advocated that.
People who practice Judaism are called Jews.
There are no churches in Judaism.
Followers of Judaism are called Jews.
The people who follow Judaism are called Jews.
Clergy for Judaism are called rabbis.
A member of Judaism is called a Jew or a Jewish person.
If you mean "Judaism", they are known as "Jews".
People who follow Judaism are called Jews
Judaism is not a centralised religion and does not have a single leadership. The members of Judaism are called Jews.