The band name means a female trepang, or sea cucumber (adding an inflexional '-a' at the end of a word in Russian makes it feminine). It was chosen because on the day of forming of the band (11th December 2001) a huge drop of trepangs was registered on the Japanese island of Shikoku and, as a word, trepang sounds bouncy and is unfamiliar to most people.
Some of Trepanga's members are more known to the audience as actors in various Moscow theaters.