Before a Jew is born, he is made to swear (promise) to live up to his full potential and resist evil to fulfill his mission on earth. The book Tanya begins exactly with this “mission statement” and the name Tanya literally means “we have been taught”. Alter Rebbe, the book’s author, didn’t pick the name at random. In fact, he did it for a couple of reasons.
1. There exist a great many unclean shells (klipos) that dull people’s hearts. One of them in particular, impacts those that are engaged in Torah study. This klipa “backs up” the hearts of the learners and prevents them from touching the secrets of the Torah, instead filling them up with pride and self-satisfaction in trying to persuade them to be content with the Torah’s simple meaning. The name of the klipa is Tanya - תניא
The struggle with this klipa is carried out through learning the Torah’s secrets, ergo: the book’s name, as if to hint that learning it enables us to struggle with this particular klipa,
2. If the letters in the word Tanya are rearranged, we get the word “eitan”. The word has several meanings: mighty, stalwart, etc. The commentators add that parenthetically it refers to the spark of Jewishness, an undissolvable godly essence in every Jew.
Thus the name Tanya combines two ideas: struggle with a klipa and the positive, unyielding might of the Jewish soul.