Recently I have been made aware of many people who are in the conversion process who already call themselves Jews. By "in the process" I mean that they're beginning to learn Hebrew, doing Torah study with a Rabbi, attending services on Shabbat. Some are keeping kosher, tzniut, and are Shabbat observant. I should mention that the potential converts in question are women, so there would be no circumcision. As far as I know, there has not been any immersion in a mikvah. I don't know if it's important to mention that they are not seeking orthodox conversions- some reform, some conservative- but none that I know of are prepared to convert with an orthodox rabbi.
My question is: When can somebody in the process of conversion refer to themselves and expect for others to refer to them as a Jew? Also, are they recognized as converts while they are in the process of conversion, or is that a title that comes after the conversion has been completed?