Companions are a critical aspect of Code Vein. They heal the player, distract potentially difficult enemies, and hit pretty hard in combat. Their constant dialogue may wear thin, but their usefulness outweighs their repetitive quips.
The ability to woo and establish a romantic relationship with NPCs is a common one. With Fire Emblem: Three Houses‘ success, romance is on everyone’s mind when starting a new game with detailed companion characters.
When a game offers AI characters as companions, one of the first questions fans ask is, “will there be romance?” The short of it is: no. There does not appear to be romance in Code Vein. Based on a similar question appearing as far back as 2018 and reappearing again during the beta in July 2019, and again as the official release neared, there is no indication of romantic potential with any of the companions.
Based on my, incomplete experience with the game and Reddit topics, you can cultivate friendships, but not romantic relationships with the characters.
It is mildly misleading to call it relationship building when it comes to companions and support characters at the Home Base. It serves a minor purpose, but a good one for the game. If the player character brings desired valuables to NPCs, they will receive higher quality items in return. For instance, if you give Coco her preferred items, she will eventually reward you with the Mercury Blood Code.
So while there is no indication of romantic options in Code Vein, you can befriend the characters for higher quality items.