Faolin was one of Arya's guards when she ferried Saphira's egg between the Varden and the elves. She was in love with him, and was deeply upset when he was killed when Durza ambushed them.
Any mention of Faolin are memories- oftentimes reminders from Arya to Eragon that she does not love him.
Eragon, Saphira, Murtagh, Brom, Arya, Faolin, Glenwing, Roran, Katrina, Angela
I think that Arya either loved her companion Faolin(who was killed in the book, Eragon, in the ambush by Urgals) or she might actually like him, she just doesn't want Eragon distracted from his duties or fate. If I were Paolini I would have Eragon fall in love with, like, some long-lost daughter of Angela's. I don't know, Angela is awesome.
In the "Guardians of Ga'Hoole" book series, Arya does have feelings for Faolan, but it's more of a friendship and mutual respect rather than romantic love. Their bond grows stronger as they face challenges together and support each other through their adventures.
My personal favorites are... Cliff-Twig-Branch-Rowan-Buck-Dire-Finch-Cody-Grizzl-Spark-Dipper-Rooster-Puddle ...Some are a bit more 'playful', but they're unique and could give your wolf personality.
So far, and presumably, Arya only regards Eragon as a friend. However, it is somewhat hinted that she may have possibly had some feelings for her deceased elf friend Faolin, who was apparently killed along with another fellow elf friend when they were ambushed by the Shade Durza while escorting Arya as she ferried Saphira's egg between their own elf people and the Varden. Other than that, we will probably find out more about the true answer in the fourth book of the Inheritance Cycle.