Something I loved about Death Note was the characters, and you get no better character evolution (imo) than in Monster. 10/10 series, one of the best plots I've ever encountered.

I'm going to recommend manga rather than anime since I barely watch anime but read a lot of manga. Some of these do have an anime adaptation.
Absolutely Kaiji and Akagi. Fukumoto is the best when it comes to human behaviour and psychological battles, but most of his stuff doesn't have an anime. Since it's only one volume, try reading Confession, if you like it you'll probably like everything else by Fukumoto.
Aside from that, Monster is kind of similar to Death Note if you squint your eyes, and you might also enjoy Home Hero, One Outs and Liar Game.

Hyouka is also a detective-ish story, albeit with much lower stakes.

Attack on Titan's best fights rival the best moments of Death Note in terms of their documenting of thought processes and how victory is demonstrated, IMO.

No Game No Life has the slightly goofy aspect to it and lots of "'smart' person gains the upper hand through insane maneuvering," though it's fundamentally a comedy.

And if you're interested in comedy (and romance), Kaguya-sama: Love is War (especially the earlier seasons) fully commits to the "psychological battle of wits" gag.

Kaiji: Ultimate Survivor

Promised Neverland season 1