The name Good Heart in Chinese / Japanese...

佛心 means the Buddha's mind, Buddha-heart, or the spiritually enlightened heart/mind.

The Buddha Heart is detached from good and evil and other such constructs. The Buddha Heart has mercy, compassion, and loving-kindness for all sentient life, the good, the wicked, and all in between.

The heart and mind (心) are the same concepts in the ancient Orient, so you can use heart and mind interchangeably in this context.

關心 means caring in Chinese.

Caring is giving love and attention to people and things that matter to you and anyone who needs help. When you care about people, you help them. You do a careful job, giving your very best effort. You treat people and things gently and respectfully. Caring makes the world a safer place.

Note: 關心 is also a word in Korean Hanja, but in Korean, it means taking interest or concern. In Korean, it's still a good word, but it doesn't quite have the “caring for a person” meaning that it does in Chinese.

See Also:  Benevolence | Altruism

專心 makes a word that means “paying attention with your heart.”

It's often translated as “dedication,” as in “be absorbed in” or “concentrate one's efforts.” It's also used to mean “with the single mind,” “whole-heartedly,” “paying attention,” “undivided attention,” “concentration (-ed),” “engrossed,” “devotionally (listening/watching),” and/or “attentive.”

The first character means “for a particular person, occasion, or purpose,” “focused on one single thing,” “concentrated,” and sometimes, “special.”

The second character means “heart” or “mind” by itself.

My favorite translation, which comes from the Oxford Advanced Chinese/English Dictionary, is, “wholehearted devotion.”

If it seems like the meaning of this word is quite open, you are correct. The context in which the word is used matters a lot. It can mean different things depending on how you use it. This makes it kind of nice as you can decide what this means to you (within some limits). This is always positive in meaning, so even if a Chinese person reads it differently than you, it will still have a good meaning.

In Japanese, they tend to use a variation of the second character which has one less stroke. If you want your calligraphy written this Japanese form, please click on the Kanji shown to the right instead of the button above. Note: Japanese and Chinese people will recognize either form.

See Also:  Faith | Devotion

善心 literally reads “Good Heart” but is used to refer to the ideas of kindness, benevolence, philanthropy, virtuous intentions, moral sense, and conscience.

Some will also translate this as the morality of mind (as the character for the heart is often used to mean mind).

In Japanese, this can be the given name Yoshinaka.

In Japanese, 無心 means innocent or without knowledge of good and evil. It literally means “without mind.”

無心 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: “No mind, a mind without ego. A mind like a mirror which reflects and dos not judge.” The original term was “mushin no shin,” meaning “mind of no mind.” It is a state of mind without fear, anger, or anxiety. Mushin is often described by the phrase “Mizu no Kokoro,” which means “mind like water.” The phrase is a metaphor describing the pond that clearly reflects its surroundings when calm but whose images are obscured once a pebble is dropped into its waters.

This has a good meaning in conjunction with Chan / Zen Buddhism in Japan. However, out of that context, it means mindlessness or absent-mindedness. To non-Buddhists in China, this is associated with doing something without thinking.
In Korean, this usually means indifference.

Use caution and know your audience before ordering this selection.

More info: Wikipedia: Mushin

精神 is the kind of spirit you have if you perform well in sports or competitions. It is the idea of having a good attitude and putting your all into something - so much so that others can see or feel your spirit. It is the essence of your being that can only be subjectively described because there are no words that can fully explain what “spirit” really is.

For your information:
My Japanese dictionary further tries to explain this word by comparing it to mind, soul, heart, or intention.
My Chinese dictionary compares these characters to meanings like vigor, vitality, drive, and mentality.
My Korean dictionary defines this as mind, spirit, and soul.

See Also:  Vitality | Heart | Soul

禪心 represents an image of your meditation coming from and filling your heart.

The meaning of the first character is “meditation” and the second character is usually defined as “heart” or sometimes “mind.”

There is a two-fold meaning here, as a good meditation session must start with a centered heart or mind. Yet at the same time, meditation serves to cleanse, focus, and center the heart and mind.

聖心会 is the Japanese martial arts title “Seishinkai” or “Seishin-Kai.”

It literally means “Sacred Heart Association” or “Pure-Heart Club.”

聖 can mean holy, sacred, saint, sage, virtuous, expert, wise and good, upright, or correct.
心 can mean heart, mind, center, core, spirit, soul, or vitality.

聖心 creates a word meaning sacred heart, or the holy mind (that of Buddha).
会 in Japanese means association, club, meeting, assembly, party, gathering, conference, athletic meet, or society.