Nuala is a shortened form of the name Fionnuala
In Irish mythology Fionnuala was the daughter of the sea god Lir. She and her brothers were turned into swans for 900 years by their step-mother. Throughout the 900 years Fionnuala guided her brothers, keeping the family together and maintaining their hope that their curse would eventually be lifted.
The tale shows Fionnuala's love and loyalty for her family, as well as her ability to endure and remain hopeful through hardships.
I believe these qualities match well with what we have seen of Nuala so far. We know she managed to endure being Under the Mountain with her sister and Rhys, and she has shown great loyalty as a spy for both Rhys and Azriel.
I look forward to seeing more of her in the next book