Gilina

Gilina Renaez was a character on the Sci-fi television show, Farscape. She was a non-combat Peacekeeper, who was a technical specialist in maintenance and engineering. She was part of a salvage crew sent to an ancient derelict ship, the Zelbinion. They were attacked, and she was the sole survivor. She was found there by Crichton and the crew of the Moya. She helped them to repel the same attackers, and had some romantic moments with Crichton. She stayed behind to be rescued by the Peacekeepers, rather than join the crew of the Moya. She later encountered Crichton and Aeryn at Gammak Base, where she helped them get past security, and later flee the base. She was mortally wounded in the process, and died on the Moya.

Gilina is an invented name, and has never appeared in the SSA's name database. Gilina is a unique alternative to Gillian, and I think it's a perfect example of a unique name that is not too weird.