We learn from the beginning of Parashas Shemos that the Israelites maintained their identity by keping only three things: we kept our Hebrew names, maintained distinct clothing and spoke Hebrew. From the outset that seems okay.
However, things were still very bad and the Israelites were still on the brink of complete assimilation. Rabbi Yitzchak Feigenbaum of Tiferes Bais Yaakov in Toronto mentions something unique (I heard this from someone that heard him speak): that we must be mindful that THIS WAS ALL THEY HAD.
For example, in Israel today you have many secular Israelies doing the worst things imaginable but still keeping their Jewish names and “modern” Hebrew language. I also remember hearing about how in the Soviet Union, when all traces of Jewishness were shunned, Jews kept an identity by watching Yiddish theater. Yiddish theater was a non-religious way to show off Jewish customs and folkways and would entertain on any given day, especially Shabbos, Yom Kippur and all Jewish holidays. Still, this was that they to hold onto and allowed some to embrace a Jewish, if not Torah, lifestyle after the collapse.
As controversial as this might sound, if we were to cast off Jewish names, clothes and language in favor of all the other Mitzvos, we would be okay. It was said that Rabbi Yoel Teitelbaum, the late Satmar Rebbe, advocated taking on non-Jewish names for legal purposes to supplement Jewish names. For example, Rabbi Yoel changed his name, albeit not by much, from Yoel to Joel.
However, let me be clear: Having those three traits are very important, as long as they are accompanied by everything else that’s Jewish.