Amari is a name that's rising in popularity in the US for both boys and girls. Last year, about 1000 baby girls and 2000 baby boys were named Amari in the US, making it one of the Top 20 gender neutral names.
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Amari has a number of possible cultural origins and positive meanings. Amara is another possibility for girls.

Amari

A multicultural unisex choice that peaked for girls at the same time as Amy. <em>Ami</em> is also the French word for "friend."

Anime

Many things to many peoples: a flower name, also spelled Hanae, to the Japanese; a Czech and Polish short form of Johana; and an alternate form of the biblical name Hannah in the US. It also means "craft, work" in Hawaiian and "glow" in Maori.

Hana

Haru

Hito

Hitori

Kawaii

Keitai

Kiiro

Kintama

Kirei

Kuro

In Japan, color names symbolize human qualities (in this case, fame); name of gifted violist Midori, but also a Japanese melon liqueur. 

Midori

Murasaki

Natsu

Nene

Raidon

Lovely Japanese name that would certainly be appreciated in Europe and the U.S. It was rarely used in Japan until the 1990s, and draws its current popularity from the fact that it is deeply connected to Japanese traditional culture without sounding frumpy and old-fashioned.

Sakura

Shiro

Sutekina

Tora is the female version of Tor or Thor, the name of the Norse god of thunder. Actress Jeanne Tripplehorn chose it for her daughter. 

Tora

A more modern nickname for Victoria than Vicky, Tori is used fairly frequently on its own, kept in the public eye by singer Tori Amos and actress Tori Spelling. Still, it's far from fashionable, sinking in the polls significantly since reaching a peak of Number 142 in 1994.

Tori

Aurra's list "Japanese Word Names" of 23 great name ideas: Amari - Tori!

Japanese Word Names

Word names are all the rage these days. But if you don't want your kid to be one of the many nouns in his/her classroom but like the meanings, looking to words in other languages might help. An exotic language such as Japanese can provide many alternatives to virtue and word names but mean the same thing. They also have the added value of Kanji script.