It only belongs to him in the party you control.
And even if that's not 100% accurate considering the whole saga, his story and the events arround him were unique even if he was not the only Bhaalspawn in the world.
Sarevok and the other Bhaalspawn (included imoen) didn't have the same story.
If every companions had started in candlekeep, were a bhaalspawn, were attacked by Sarevok's assassin's, were captured by Irenicus for its power, became the slayer and so on... charname would not have been interresting at all in the story.
And if you had Imoen in the party, then you had two Bhaalspawn you controlled as a player and they'd go through the adventure together. As for their special abilities, I'd take Imoen's ability to be resurrected over the slayer change (which I've found useless except for reputation management), if the game would let you choose. And I didn't find charname interesting to begin with. Everyone got the same background, same adventure (since the main plot was linear for the most part), only different strongholds and romances. Except if you prefer to play female characters, then you didn't, because your only option was Anomen.
By comparison in BG3 my drow druid felt very different than my githyanki wizard.
1) Create entirely unique background tags for custom characters based on their place of origin. We already have the Baldurian tag. Add in a couple other locales, the most obvious ones being Waterdhavian and possibly Chult.
You already get that to some extent with drow, since disguising yourself as one doesn't give you all of the special conversation they get, and there are no drow companions. So it should be possible to expand on that.
