In the English version, people often precede Relena's name with "Miss", which is a respectful way of refering to a girl, young woman, or a woman who is unmarried. My thought is that the "Miss" is used because she is the daughter of the Vice Foreign Minister. It is also used by Noin and Quatre, who seem to be in the habit of addressing a respected person by title.
In the Japanese version, Noin calls her Relena-sama (the addition of "sama" indicates a very high respect), and Quatre often refers to her as just "Princess". Duo's name for Relena seems to be "Ojou-san", which means "lady" in Japanese. It's also commonly used when referring to a rich and/or popular girl, which would be appropriate as well, I suppose.
The only people, as far as I can remember, who call Relena by her first name (without the added suffixes or prefixes) are Heero and Zechs. In Japanese, only people who are very close to someone call them by their first name alone. Calling somebody by their first name when you aren't close to them is seen as insulting and somewhat presumptuous in their culture. This further helps to clarify the relationship between Relena and the two young men. Heero starts calling her this in the second episode, which may have been seen as kind of rude. But then again, Relena just calls Heero by his first name as well.
The name analysis wouldn't be complete without the overly popular Kabalarians entry, so without further delay . . . the name of Relena creates a friendly, sociable, charming nature, but causes you to be too easily influenced by others. While you find it easy to meet and mix, and can appear agreeable and compromising in conversation, you can become unbending and forceful if pressed too far. Others learn that you cannot be told what to do and you seldom change your mind once it is made up. You prefer situations that allow a degree of independence, but are reluctant to take on a demanding work-load or responsibility. (Most of this, obviously, is pretty inaccurate. Oh well.)
Relena's name, I've discovered, is not a very common name in English-speaking countries. However, I did find a similar name that could have the same meaning. I think that maybe the name "Relena" originated from the English name "Regina", which means "queen" in Latin. I think this fits Relena very well, since she herself was a queen at one time. It also hints at the royal status she's had since birth (being the princess of the Sanc Kingdom).
Now, for the reason for my arrangement of Relena's last names. I just thought it made more sense, since she used to be a Peacecraft but took her adoptive father's name at the end of the series instead. Besides, she was a Peacecraft before she was a Darlian. I think that because of these reasons the form I use is more accurate. Thus, Relena Peacecraft Darlian.