YOU SAID:

my name is nonexistent

INTO JAPANESE

私の名前は存在しません

BACK INTO ENGLISH

My name doesn't exist

INTO JAPANESE

名前が存在しません

BACK INTO ENGLISH

Name does not exist

INTO JAPANESE

$name$ はありません。

BACK INTO ENGLISH

$name$ does not exist.

INTO JAPANESE

$name$ はありません。

BACK INTO ENGLISH

$name$ does not exist.