There are a whole bunch of other people floating around in Altered Carbon Season 1, who play integral but sometimes confusing roles in the plot.

Laurens Bancroft: The super-rich Meth who makes a deal to get Takeshi out of cold storage to enlist him in solving Bancroft's murder. Bancroft was so rich that he not only can afford clones of his original body to resleeve his stack into, he has a dedicated satellite in orbit, which holds a backup copy of his consciousness--so even if his stack is destroyed, he can live on. Just before the start of Season 1, Bancroft's sleeve was murdered and his stack destroyed. When he redownloaded from his satellite, he set about trying to figure out who killed him. (There are a lot of suspects, including his extremely crappy family.) Turns out that Bancroft killed himself, though, after committing a murder and being blackmailed by Rei. He destroyed his own stack out of shame, minutes before his scheduled backup, so that when his consciousness was downloaded again from the satellite, he wouldn't remember what he'd done.

Vernon: Tak found Vernon by investigating death threats against Bancroft, who blamed Bancroft for his daughter Lizzie being beaten and driven to madness. When Tak confronts and interrogates him, he makes Vernon an ally by helping him try to treat Lizzie's psychological problems, with Poe's assistance. Vernon becomes an ally of Tak's and helps him in his fight to solve Bancroft's murder and take down Rei.

Lizzie: Vernon's daughter Lizzie was a sex worker who was visited by Laurens Bancroft, and eventually got pregnant by him. When she went to his house to tell him about it, Lizzie was confronted by Bancroft's wife, Miriam, who feared the threat of an illegitimate Bancroft child and nearly killed Lizzie. Miriam enlisted Rei to have Lizzie driven insane with virtual reality torture, fragmenting her mind. Vernon kept Lizzie in VR to protect her, and Tak and Poe worked to help Lizzie recover. When she did, Tak learned about what had happened, revealing another piece of the puzzle regarding Bancroft's murder and Rei's involvement.

Ortega: A police officer who worked with Tak on Bancroft's murder, and was in love with the man who owned the body Tak inhabits in Season 1. She was the officer originally assigned to Bancroft's murder, but ruled it a suicide against Bancroft's wishes. She spends the first season of Altered Carbon helping Tak as he works to solve the mystery, and they develop a close relationship. Ortega was formerly a Neo-Catholic--according to her faith, she could never be resleeved due to her beliefs. She renounced her religion, however, which causes strain between Ortega and her family.

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Netflix's Altered Carbon Season 2: Season 1 Recap - Story And Characters To Remember - GameSpot