In 1845, James Howlett, a boy living in Canada, witnesses his father being killed by groundskeeper Thomas Logan. The trauma activates the boy's mutation: bone claws protrude from his knuckles, and he kills Thomas, who reveals that he is James's real father. James flees along with Thomas's son Victor Creed, who is thus James's half-brother. They spend the next century as soldiers, fighting in the American Civil War, both World Wars, and the Vietnam War. In Vietnam, Victor attempts to rape a Vietnamese woman, and kills a senior officer who tries to stop him. James defends Victor and the two are sentenced to execution by firing squad, which they survive. Major William Stryker approaches them in military custody, and offers them membership in Team X, a group of mutants including Agent Zero, Wade Wilson, John Wraith, Fred Dukes, and Chris Bradley. They join the team for a few years, with James now using the alias Logan, but the group's (especially Victor's) disregard for human life causes James to leave.
Six years later, James (now using the name Logan) is working as a lumberjack in Canada, where he lives with his girlfriend Kayla Silverfox. Stryker and Zero approach Logan at work. Stryker reports that Wade and Bradley have been killed, and he thinks someone is targeting the team's members. Logan refuses to rejoin Stryker, but after finding Kayla's bloodied body in the woods, Logan realizes Victor is responsible. He finds him at a local bar, but Logan loses the subsequent fight. Afterward, Stryker explains that Victor has gone rogue, and offers Logan a way to become strong enough to get his revenge. Logan undergoes a painful operation to reinforce his skeleton with adamantium, a virtually indestructible metal. Once the procedure is complete, Stryker attempts to betray Logan by ordering that his memory be erased, but Logan overhears this and escapes to a nearby farm, where an elderly couple take him in. Zero kills them the following morning and tries to kill Logan. Logan takes down Zero's helicopter, killing him, and swears to kill both Stryker and Victor.
Logan locates John and Fred at a boxing club. Fred explains that Victor is still working for Stryker, hunting down mutants for Stryker to experiment on at his new laboratory, located at a place called "The Island". Fred mentions Remy "Gambit" LeBeau, is the only one who escaped from the island and therefore knows its location. John and Logan find LeBeau in New Orleans, then both fight Victor, who kills John and extracts his DNA. Agreeing to help release mutants that Stryker has captured, Gambit takes Logan to Stryker's facility on Three Mile Island. Logan learns that Kayla is alive, having been coerced by Stryker into keeping tabs on him in exchange for her sister's safety. However, Stryker refuses to release her sister and denies Victor the adamantium bonding promised for his service, claiming that test results revealed Victor would not survive the operation. Stryker activates Wade, now known as Weapon XI, a "mutant killer" with the powers of multiple mutants, who he refers to as the "Deadpool".
While Logan and Victor join forces to fight Weapon XI, Kayla is mortally wounded leading the Island's captive mutants â including a teenager named Scott Summers â to safety. The mutants are subsequently rescued by Professor Charles Xavier. Logan decapitates Weapon XI, destroying one of the cooling towers in the process. Stryker arrives and shoots Logan in the head with adamantium bullets, rendering him unconscious. Before Stryker can shoot Kayla, she grabs him and uses her mutant power to persuade him to turn around and walk away until his feet bleed. Logan regains consciousness but has lost his memory. He sees Kayla's body, but does not recognize her, and leaves the island.
In a mid-credits scene, Stryker is detained for questioning by some MPs in connection with the death of his superior, General Munson, whom Stryker did in fact kill after Munson declared his intention to shut down Stryker's project. In a post-credits scene, Logan tells a Japanese barmaid he's "drinking to remember". In another, Deadpool is shown to still be alive.

Question: What is the name of Logan's girlfriend that he lives with while working as a lumberjack?
Answer: His girlfriend's name is Kayla Silverfox.
Alternative answer: Kayla