Rinoa's name is very unique and beloved. The name doesn't have any meaning or sign to the character, it was made to be open and fitting her personality on some way's as what Kazushige Nojima wanted to create.

Systematically the English translation of Rinoa is somewhat different then the Japanese one.  Rinoa's name is written in the Katana Characters, so her name should somewhat look like this: リノア   ハーティリー 

Rinoa's name isn't from Japanese foreign, why it is isn't known, yet lately most character get names that doesn't have any social meaning to it's origin.

Like Squall no real reasons have been given why Rinoa was named with this name. The name does not have a meaning, it is made in English pronunciation.

It's isn't difficult to pronounce the name Rinoa. It is said that you can pronounce Rinoa on two way's. The first one is reading it how it is written and the second is a slight higher march on the "I" part like how "I" is pronounced in a single form.

Yet, Square-Enix do have it's alternative on how this name is pronounced. Squall calls the name Rinoa at the ending scene, by matching the name into his lips movement, you can tell that Rinoa has to be pronounced by how it is written, not by the higher "I".

Many noticed the surname change of Rinoa in the game. Heartilly isn't her real name, it's her mother's maiden name. Reasons for this can be seen in the eternal squarrel between father and daughter. Not wanted to be recognized as Fury's daughter, she changes her name in her mother's maiden name.

Like her first name, Heartilly is also from the English pronunciation. rumours do the round that Heartilly may have been taken from Lockheart, the female lead from the previous game. Not is sure why, yet resamblance between these two girls are great and share the same feelings to one another.

This was found here

Although the name Rinoa creates an interest in the deeper aspects of life, we emphasize that it frustrates you through a scattered and emotional nature. This name, when combined with the last name, can frustrate happiness, contentment, and success, as well as cause health weaknesses in the heart, lungs, bronchial area, liver, and bloodstream.

Your first name of Rinoa has made you happiest when you are expressing in some creative, artistic way, and not conforming to strict routine. In a large group of comparative strangers, you are quiet and rather shy, unable to express yourself, not really wanting to become involved in conversation. On the other hand, among friends with whom you feel at ease, you are expressive, witty, and quite charming. These contrasting natures make it difficult for people to understand you and can lead to friction in your personal life. You are deep, philosophical, and refined, but your extremely sensitive nature causes you to become depressed and self-pitying over any real or imagined slight.  

Opinion

Like my opinion in the Squall part, I can say I both agree and dissagree. It may give Rinoa happiness and success, yet she isn't weak in her heart nor sickness. Yes, Rinoa is a standard and healty girl and contrast her life with the nature as may be charming and expresses her feelings most of the times. The name Rinoa does not have a meaning, yet it symbolizes her strengt, weakness and charmed nature.