In 1944, with the help of Russian mystic Grigori Rasputin, the Nazis build a dimensional portal off the coast of Scotland and intend to free the Ogdru Jahad—monstrous entities imprisoned in deep space—to aid them in defeating the Allies. Rasputin opens the portal with the aid of his disciples, Ilsa von Haupstein and Obersturmbannführer Karl Ruprecht Kroenen, member of the Thule Society and Adolf Hitler's top assassin. An Allied team is sent to destroy the portal, guided by a young Trevor Broom, who is well-versed in the occult. The German team is killed and the portal is destroyed—in the process absorbing Rasputin—while Haupstein and Kroenen escape. The Allied team discovers that an infant demon with a right hand of stone came through the portal; they dub him "Hellboy" and Bruttenholm adopts him.
Sixty years later, FBI agent John Myers is transferred to the Bureau of Paranormal Research and Defense (BPRD) at the request of Broom and he meets the adult Hellboy and a psychic, amphibious humanoid named Abe Sapien. He learns that a third BPRD member, Liz Sherman, has recently checked into a mental hospital to protect others from her volatile pyrokinetic abilities. Despite regular visits and coaxing from Hellboy, she is determined not to return. Kroenen and Haupstein resurrect Rasputin in the mountains of Moldova and the three unleash a hellhound known as Sammael. Rasputin imbues Sammael with the power to reincarnate and split his essence, causing two of the creature's eggs to hatch and mature each time one dies. Rasputin visits Liz as she sleeps, activating her powers and almost destroying the hospital. Myers convinces her to return to the Bureau.
Sammael's ability to multiply becomes a problem, as Hellboy repeatedly kills it, dozens are born. Concluding the eggs are in the sewer, Hellboy, Abe and several FBI agents go down the sewer to destroy them. Abe is injured while looking for the eggs, Kroenen kills most of the agents. Kroenen, whose mutilated body is run by mechanical parts, shuts himself down, pretending to be defeated. Kroenen's body is brought to the bureau. FBI Director Tom Manning is angered by Hellboy's recklessness. Myers takes Liz out for coffee and to talk. Hellboy, jealous, covertly follows them, leaving the bureau unguarded. Kroenen reanimates himself and Rasputin appears at the bureau, confronting Professor Broom. Rasputin offers him a vision of the future, showing Hellboy is the agent that will destroy the world. Broom is stabbed in the neck by Kroenen and dies clutching a rosary.
Manning takes over the B.P.R.D. and locates Rasputin's mausoleum in an old cemetery outside Moscow, Russia. A team led by Manning and Hellboy enter the mausoleum, but swiftly become separated. Hellboy and Manning find their way to Kroenen's lair and defeat him. Hellboy reunites with Liz and Myers at Sammael's new nest, but the creatures overwhelm them. Liz uses her pyrokinetic powers to incinerate the Sammaels and their eggs. Hellboy, Liz and Myers lose consciousness and are captured by Rasputin and Haupstein. Rasputin sucks Liz's soul out of her body, then tells Hellboy to release the Ogdru Jahad in return for her soul. Hellboy awakens his true power as Anung un Rama, causing his horns to regrow, and begins to release the Ogdru Jahad. Myers breaks out of his restrain, subdues Haupstein, and reminds Hellboy that he can defy his destiny. Remembering his true self and what Bruttenholm brought him up to be, Hellboy breaks his horns, reseals the Ogdru Jahad and stabs Rasputin with one of his broken horns.
Rasputin has been possessed by a creature from the Ogdru Jahad. The tentacled Behemoth bursts out of his body and grows to immense size, killing him and Haupstein. Hellboy allows himself to be swallowed by the beast, then detonates a belt of hand grenades and destroys it from the inside. He whispered something in Liz's ear and she is revived. When she asks how her soul was returned, Hellboy replies that he threatened to come to "the other side" to claim it back. Liz and Hellboy share a kiss.

Question: Why do they name the infant "Hellboy"?
Answer: The infant is a demon that came through the portal.
Alternative answer: Because he comes through a portal from hell.