With 8 707 bearers, Tenzin is the 18th most common given name in Bhutan (2014 Data). About 72% of bearers of this name are Male in Bhutan (2014 Data).Source: https://forebears.io/forenames/tenzin
I think that Tenzin is a very nice and classic Tibetan and Bhutanese name. I like it on both genders. This is one of the given names of the 14th Dalai Lama, Tenzin Gyatso.
Tenzin is a character in The Legend of Korra, The upcoming spinoff of Avatar: The Last Airbender. He is the son of Aang and Katara, two main characters from the original show.
The character Tenzing Tharkay from Naomi Novik's Temeraire series of books bears a variant of this name; he's an adventurer of Nepali and English descent who first appears in the book Black Powder War.
https://en.wiktionary.org/wiki/%E0%BD%96%E0%BD%A6%E0%BE%9F%E0%BD%93%E0%BC%8B%E0%BD%A0%E0%BD%9B%E0%BD%B2%E0%BD%93
Also pronounced as /tɛnˈzɪn/ in English
https://en.wiktionary.org/wiki/Tenzin [noted -ed]