Tanya is the Slavic hypocoristic of Tatiana. It is now quite commonly used as an independent given name in the English-speaking world.
Tanya is also of Hebrew origin derived from the Aramaic term meaning ‘it was taught in Baraita’ which is Biblical teaching. Within Hasidic Judaism this refers to the Oral Torah. It is the first word used within the Tanya. 
Its popularity grew in many respects thanks to Alexander Pushkin‘s poem Eugene Onegin whose main character was Tatiana Larina, beloved by Onegin.
Variants include Tania, Tanja (Serbo-Croatian, German, Danish, Estonian, Finnish, Dutch, Macedonian and Ukrainian), Tanea (Romanian), Táňa (Czech) or Taanya (Levant and Indian subcontinent) 
It is the 237th most common name in the United States according to namestatistics.com, which uses US Census data.