Profile of a lady
Through the years, not much has really changed when it comes to Rosa. Square did a great job at keeping her character true to her form in the various incarnations the game has taken, with only a few changes here and there to gameplay-related specifics.
A textbook definition
Name: Rosa Farrell
Class: White Mage
Gender: Female
Age: 19
Height: 162 cm / 5'4"
Weight: 47 kg / 104 lbs
Dexterity: Right Handed
Birthplace: Baron
Skills: Fight, White, Pray, Aim, Item
Weapons: Bows and Staves
Rosa grew up in Baron alongside Kain and Cecil, her childhood friends. She follows in the footsteps of her mother, who once defended the knights of Baron as a white mage. He studied white magic from a very young age, and seeks to fight alongside Cecil, just as her mother did for her father. Besides that, she's a master of archery, which makes her self-sufficent in battle. She is very strong willed and adamant. Rosa tends to be very reserved, yet she has moments when she surprizes even Cecil.
A little deeper look
Rosa is a woman driven by her love for others around her. Whether it's for Cecil or for her friends throughout her journey, she strives to care for and protect them. She mainly plays a supportive role, both in plot and game mechanics. However, she is really a vital part of Final Fantasy IV, being one of the first heroines the US audience encountered in the series.
Rosa's personality is selfless. She puts everyone before herself. Even when it comes down to what she thinks about any given situation, she really just wants what's best for everyone, especially Cecil. Above all else, she too wants to get to the bottom of the events that transpire throughout the game and bring peace to the world. Rosa is often the voice of reason, jumping in during rough times to help ease the tension and calm fears. More than anything, Rosa is a peacemaker.
In many ways, her character may not be as deep or developed as the ones that came along later in the series. However, I don't think that makes her any less of a character. For it's time, the characters of Final Fantasy IV were really unique and deep for the genre. Furthermore, Rosa is the first love interest in the game series, something that undoubtedly drew many people to her character.
What's in a name?
Rosa is the Latin form of the name Rose, which essentially means "fame" or "kind". From early on, this word was used as an association with the Rose flower. Roses themselves have had a long history associated with love. To the Greeks and Romans, the rose was identified with the goddesses of love, Venus and Aphrodite. Rosa herself represents love. Her theme song "The theme of love" makes this quite obvious. Other than that, roses are also known for their thorns. I think this reflects her well, in that although she is beautiful and delicate, she is not to be taken lightly. She can defend herself well.
Farrell is derived from the Irish Gaelic name, O'Fearghail or otherwise known as Fearghal. The name itself means "Man of Valor". This was the name of an 8th century king of Ireland. Valor can simply be described as "boldness or determination in facing great danger". The name itself could relate to Rosa's father, a warrior. Her mother fought alongside him as a white mage. Rosa herself displays valor in many situations. Farrell is a pretty common surname, most well known for the name would be the actor Will Farrell.
Middle name: Joanna Rosa has a middle name, as revealed in a novelization of the game's story released by SquareEnix at the time of the GBA release. Joanna is revealed to be Rosa's mother's name. This name is derived from the name John, which means "God is Gracious".
Rosa in Battle
Rosa really is an essential party member. In several instances throughout all of the various play-throughs, it's always come down to Rosa keeping the party alive. Later in the game, she gains strong defense through equipment and stats which help to keep her (and usually Cecil) standing while everyone else is down.
First and foremost, Rosa is a white mage. She is capable of using some very helpful white magic spells that aid the party, and later can deal a signifigant amount of damage with her Holy spell. Beyond that, her Pray ability comes in handy by restoring a bit of HP and precious MP. White mages in the story are primarily from Mysidia. However, when Devil's Road was built, Baron began to enlist both white and black mages with their army. Rosa's mother trained as a white mage, and later Rosa followed in her footsteps.
Rosa is also an archer, she can equip both bows and staves. Bows are actually very useful in various circumstances in that her Aim skill can be used as a decent attack. Although it doesn't deal the amount of damage that Cecil, Kain, Edge, or Yang can, it can still pack an extra punch during random encounters or helping to finish of a boss quickly.