Going very strictly based off my real self:
Name: Louisette
Race and Class: Human Mage
Background:
Born into an upper middle class Orlesian family. She enjoyed Orlesian ways of life and relished in the finer things and fashion. Magic powers weren't realized until mid teens (very late) so memories of family and normal life are maintained. Lived in an Orlesian circle until the war broke out. While at the circle Louisette secretly studied shapeshifting magic because the templars would punish it because it would make it easier for mages to escape the circle and harder to track down. She specializes in different feline forms due to her ridiculous love of cats.
When the circle fell apart Louisette didn't affiliate with any mage faction and kept to herself and out of sight of templars and mages who would force their will upon her. She hid by spending most of her days in the form of a domestic house cat. She would actually first meet the Inquisitor in this form. Due to her excessive amount of time roaming around as a cat she sometimes meows when talked to as well as hisses at enemies in battle.
Personality:
Generally Louisette is a loyal rule follower with a respect for authority and has a strong sense of justice. However, she will rebel when she feels that that justice is being squandered, oppressed, or diminished. She is generally pretty shy unless she feels the need to voice her opinion about something. After the Inquisitor makes the attempt to earn trust and get to know her she will open up and be very friendly and supportive. She's also pretty much a crazy cat lady.
When it comes to the templar vs. mage conflict she takes sides with each situation. She believes that in most cases the templars have become too strict, but dislikes the mages that have taken their rebellion too far. Generally wants to help restore balance to Thedas.
Biggest Annoyance:
She will force the Inquisitor to accept any quests pertaining to cats (anyone remember the seneschal script?) if she is in the party.
Relations:
Varric: Will get along handsomely and joke around, he'd probably call her something like "Whiskers."
Cullen: Would have a major crush on him unless the Inquisitor pursued romance with her. Would be secretly jealous if the Inquisitor romanced Cullen.
Vivienne: They would get along in their sense of how they think mages should fit into society (Having checks and balances), but they would conflict when it comes to ambition and desire for power. Vivienne can be a little too dubious at times for her.
Cassandra: Most likely would have a sense of respect for each other, but not really like each other.
Sera: Wouldn't get along, Sera would be too rambunctious for this cat crazy lady.
The Iron Bull: His appearance kinda freaks her out and makes her nervous around him. He doesn't really get why and always tries to joke around with her unsuccessfully.
Solas: Not enough known to tell.
Scribe Girl: Not enough known to tell.
Leliana: They'd go shopping together, but they'd conflict on religious views. Leliana would also think Louisette's cat form was too cute.
Cole: She would pity him and try to be a comfort and befriend him. They'd become pals and sneak around together.
Blackwall: She would greatly admire and respect him and see him as somewhat of a father figure. They would get along and enjoy each other's company.
Dorian: They would relish in how dashing they both think they are and make sarcastic jokes together. He would encourage her to not be afraid or shameful of her magical talents and teach her to be more confident.