The name that you're referring to is actually a surname (though I've seen several people with Cozens as their first name on FamilySearch).
From what I can gather, it's not really a Russian surname, even though I found one Russian on LinkedIn with that surname. According to Ancestry and the Internet Surname Database, Cozens is a patronymic of Cousin and it is of 'early medieval English and French origin.'
The etymology of Cousin (surname) and the word can be found here:
http://www.surnamedb.com/Surname/Cousinhttp://etymonline.com/index.php?allowed_in_frame=0&search=cousin&searchmode=none
Hope this helps :)
My PNL:
http://www.behindthename.com/pnl/149249My blog:
https://maybeitisdaijirou.wordpress.com