True Heart in Chinese / Japanese...

zhēn xīn

mago koro

While these two characters literally read as "true heart" or "genuine heart," the understood meaning is sincerity, devotion, sincere, or heartfelt. Some will extend the meaning to be like, "true love." Basically, it's the idea of doing something or treating someone with genuine feelings.

真心 is valid and has the same meaning in both Chinese characters and Japanese Kanji.

Note: While not too common, this can be the female given name "Mami" in Japanese.

zhì chéng

shisei

지성

至誠 is the idea that you enter into something with the utmost sincerity and fidelity. Ideas such as devotion, honesty, and "one's true heart" are also contained in this word.

至誠 is a universal word as the Chinese, Japanese Kanji, and Korean Hanja are all identical.

wǒ xīn zhēn ài

아심진애

我心真愛 is a slightly poetic way to express this sentiment to someone.

The meaning is "My True Love" but the characters directly translate as "I/Me/My Heart/Mind True/Real Love."

Note that Chinese grammar and construction are different, so this sounds very eloquent and artsy in Chinese.
In Korean Hanja, the third character should be written differently, just let me know when you place your order if you want that version - it will still make sense in Chinese. This phrase makes sense in Korean but not commonly used.

cán xīn

zan shin

First off, this should only be used in context of Japanese martial arts. In Chinese, it's a rather sad title (like a broken heart). In Chinese, the first character alone means destroyed, spoiled, ruined, injured, cruel, oppressive, savage, incomplete, disabled. However, in Japanese, it's remainder, leftover, balance, or lingering.
The second character means heart, mind, soul, or essence in both languages.

殘心 is one of the five spirits of the warrior (budo), and is often used as a Japanese martial arts tenet. Under that context, places such as the Budo Dojo define it this way: The spirit of zanshin is the state of the remaining or lingering spirit. It is often described as a sustained and heightened state of awareness and mental follow-through. However, true zanshin is a state of focus or concentration before, during, and after the execution of a technique, where a link or connection between uke and nage is preserved. Zanshin is the state of mind that allows us to stay spiritually connected, not only to a single attacker but to multiple attackers and even an entire context; a space, a time, an event.

In modern Japan (and Simplified Chinese), they use a different version of the first character, as seen to the right. Click on this character to the right instead of the button above if you want this modern Japanese version of lingering mind / zanshin.

shou shin ryuu

This Japanese title means "right heart style" or "true mind method."

The first character means right, correct, greater, or true.

The second character means heart, mind, soul, or essence.

The third character means style, method, or some will translate it as school.

Please note, there is more than one martial arts school that romanizes as Shoshin-Ryu.