You're assuming he didn't, and with the poster they released you shouldn't assume that at all. Venom looks like Venom which means the Symbiote already took traits from Spider-Man.
My guess is they're gonna pull a Logan and keep Brock's origin with the symbiote as a past event only referenced at times (like the death of the X-Men in Logan).
Perhaps Riz Ahmed's "Life" company seeks out Brock to help him rid himself of the demon. The trailer shows Brock is back in San Francisco, which in the comic is where he went after he ended his feud with Parker.
People keep thinking this will be a complete reinvention of Venom but most of the info that's been released goes against that.
I stand by my original theory that this movie (along with Silver and Black, Morbius and Scarlet Spider) takes place in a universe where Spider-Man quit a while back. Probably 10 years. This makes the relationship between Brock and the symbiote incredibly complex because they're basically one now (#WeAreVenom) and Venom is going to be forced to actually engage in acts of heroism due to Parker's absence.