The Internet movie database, as well as the credits for The Ring spelled the name as "Samara". (
www.imdb.com )
Besides being a name, the word Samara has a few definitions:
It is also a city in central europe, and can refer as a name of somebody being from Samara.
A city of western Russia on the Volga River east-southeast of Moscow. Founded in 1586 as a stronghold to defend river trade and the eastern frontier, it was temporarily the capital of the USSR from 1941 to 1943. From 1935 to 1991 it was known as Kuibyshev. Population: 1,231,653. (
www.dictionary.com )
Samara ~ an independent dry indehiscent fruit which has part of the fruit wall extended to form a wing (i.e. not a winged seed inside another type of seed pod). See Fruits (
www.dictionary.com)
Some other interpetations (many making sense in the context of the movie) :
Samara, Hebrew, Watch or Outlook (
www.babychatter.com/sgirl.html )
Samara, Guardian ( www.baby-names-meanings.com/firstnames/girlsj-z.html )
Samara Arabic meaning To talk in the evening or night. (
www.cfimages.com/Baby/Names/girlss.html )
Samara = Protected by God (
www.maxpages.com/babynames/Names_S )